diff --git a/autotest/gcore/tiff_read.py b/autotest/gcore/tiff_read.py
index 01e1d2b0a471..d580b6f70e15 100755
--- a/autotest/gcore/tiff_read.py
+++ b/autotest/gcore/tiff_read.py
@@ -4447,6 +4447,92 @@ def method(request):
         gdal.GetDriverByName("GTIFF").Delete(cog_filename)
 
 
+###############################################################################
+# Test GTiffDataset::MultiThreadedRead() when the amount of requested bytes
+# exceed the allowed limit.
+
+
+@pytest.mark.require_curl()
+@pytest.mark.skipif(
+    not check_libtiff_internal_or_at_least(4, 0, 11),
+    reason="libtiff >= 4.0.11 required",
+)
+def test_tiff_read_vsicurl_multi_threaded_beyond_advise_read_limit(tmp_path):
+
+    webserver_process = None
+    webserver_port = 0
+
+    (webserver_process, webserver_port) = webserver.launch(
+        handler=webserver.DispatcherHttpHandler
+    )
+    if webserver_port == 0:
+        pytest.skip()
+
+    gdal.VSICurlClearCache()
+
+    tmp_filename = str(tmp_path / "tmp.tif")
+    gdal.Translate(
+        tmp_filename,
+        "data/utmsmall.tif",
+        options="-co TILED=YES -co COMPRESS=LZW -outsize 1024 0",
+    )
+    ds = gdal.Open(tmp_filename)
+    expected_data = ds.ReadRaster()
+    ds = None
+
+    try:
+        filesize = os.stat(tmp_filename).st_size
+        handler = webserver.SequentialHandler()
+        handler.add("HEAD", "/test.tif", 200, {"Content-Length": "%d" % filesize})
+
+        def method(request):
+            # sys.stderr.write('%s\n' % str(request.headers))
+
+            if request.headers["Range"].startswith("bytes="):
+                rng = request.headers["Range"][len("bytes=") :]
+                assert len(rng.split("-")) == 2
+                start = int(rng.split("-")[0])
+                end = int(rng.split("-")[1])
+
+                request.protocol_version = "HTTP/1.1"
+                request.send_response(206)
+                request.send_header("Content-type", "application/octet-stream")
+                request.send_header(
+                    "Content-Range", "bytes %d-%d/%d" % (start, end, filesize)
+                )
+                request.send_header("Content-Length", end - start + 1)
+                request.send_header("Connection", "close")
+                request.end_headers()
+                with open(tmp_filename, "rb") as f:
+                    f.seek(start, 0)
+                    request.wfile.write(f.read(end - start + 1))
+
+        for i in range(3):
+            handler.add("GET", "/test.tif", custom_method=method)
+
+        with webserver.install_http_handler(handler):
+            with gdaltest.config_options(
+                {
+                    "GDAL_NUM_THREADS": "2",
+                    "CPL_VSIL_CURL_ALLOWED_EXTENSIONS": ".tif",
+                    "GDAL_DISABLE_READDIR_ON_OPEN": "EMPTY_DIR",
+                    "CPL_VSIL_CURL_ADVISE_READ_TOTAL_BYTES_LIMIT": str(
+                        2 * filesize // 3
+                    ),
+                }
+            ):
+                ds = gdal.Open("/vsicurl/http://127.0.0.1:%d/test.tif" % webserver_port)
+                assert ds is not None, "could not open dataset"
+
+                got_data = ds.ReadRaster()
+                assert got_data == expected_data
+
+    finally:
+        webserver.server_stop(webserver_process, webserver_port)
+
+        gdal.VSICurlClearCache()
+
+
 ###############################################################################
 # Check that GetMetadataDomainList() works properly
 
diff --git a/frmts/gtiff/gtiffdataset_read.cpp b/frmts/gtiff/gtiffdataset_read.cpp
index e9f52d11f706..9d2dcb8e2931 100644
--- a/frmts/gtiff/gtiffdataset_read.cpp
+++ b/frmts/gtiff/gtiffdataset_read.cpp
@@ -349,7 +349,10 @@ CPLErr GTiffDataset::ReadCompressedData(const char *pszFormat, int nXOff,
 
 struct GTiffDecompressContext
 {
-    std::mutex oMutex{};
+    // The mutex must be recursive because ThreadDecompressionFuncErrorHandler()
+    // which acquires the mutex can be called from a section where the mutex is
+    // already acquired.
+    std::recursive_mutex oMutex{};
     bool bSuccess = true;
 
     std::vector<CPLErrorHandlerAccumulatorStruct> aoErrors{};
@@ -416,7 +419,7 @@ static void CPL_STDCALL ThreadDecompressionFuncErrorHandler(
 {
     GTiffDecompressContext *psContext =
         static_cast<GTiffDecompressContext *>(CPLGetErrorHandlerUserData());
-    std::lock_guard<std::mutex> oLock(psContext->oMutex);
+    std::lock_guard<std::recursive_mutex> oLock(psContext->oMutex);
     psContext->aoErrors.emplace_back(eErr, eErrorNum, pszMsg);
 }
 
@@ -495,7 +498,7 @@ static void CPL_STDCALL ThreadDecompressionFuncErrorHandler(
     if (psJob->nSize == 0)
     {
         {
-            std::lock_guard<std::mutex> oLock(psContext->oMutex);
+            std::lock_guard<std::recursive_mutex> oLock(psContext->oMutex);
             if (!psContext->bSuccess)
                 return;
         }
@@ -616,7 +619,7 @@ static void CPL_STDCALL ThreadDecompressionFuncErrorHandler(
     if (psContext->bHasPRead)
     {
         {
-            std::lock_guard<std::mutex> oLock(psContext->oMutex);
+            std::lock_guard<std::recursive_mutex> oLock(psContext->oMutex);
             if (!psContext->bSuccess)
                 return;
 
@@ -634,7 +637,7 @@ static void CPL_STDCALL ThreadDecompressionFuncErrorHandler(
         {
             if (!AllocInputBuffer())
             {
-                std::lock_guard<std::mutex> oLock(psContext->oMutex);
+                std::lock_guard<std::recursive_mutex> oLock(psContext->oMutex);
                 psContext->bSuccess = false;
                 return;
             }
@@ -647,7 +650,7 @@ static void CPL_STDCALL ThreadDecompressionFuncErrorHandler(
                          static_cast<GUIntBig>(psJob->nSize),
                          static_cast<GUIntBig>(psJob->nOffset));
 
-                std::lock_guard<std::mutex> oLock(psContext->oMutex);
+                std::lock_guard<std::recursive_mutex> oLock(psContext->oMutex);
                 psContext->bSuccess = false;
                 return;
             }
@@ -655,7 +658,7 @@ static void CPL_STDCALL ThreadDecompressionFuncErrorHandler(
     }
     else
     {
-        std::lock_guard<std::mutex> oLock(psContext->oMutex);
+        std::lock_guard<std::recursive_mutex> oLock(psContext->oMutex);
         if (!psContext->bSuccess)
             return;
 
@@ -808,7 +811,7 @@ static void CPL_STDCALL ThreadDecompressionFuncErrorHandler(
 
         if (!bRet)
         {
-            std::lock_guard<std::mutex> oLock(psContext->oMutex);
+            std::lock_guard<std::recursive_mutex> oLock(psContext->oMutex);
             psContext->bSuccess = false;
             return;
         }
@@ -1271,6 +1274,9 @@ CPLErr GTiffDataset::MultiThreadedRead(int nXOff, int nYOff, int nXSize,
     std::vector<size_t> anSizes(nBlocks);
     int iJob = 0;
     int nAdviseReadRanges = 0;
+    const size_t nAdviseReadTotalBytesLimit =
+        sContext.poHandle->GetAdviseReadTotalBytesLimit();
+    size_t nAdviseReadAccBytes = 0;
     for (int y = 0; y < nYBlocks; ++y)
     {
         for (int x = 0; x < nXBlocks; ++x)
@@ -1298,7 +1304,8 @@ CPLErr GTiffDataset::MultiThreadedRead(int nXOff, int nYOff, int nXSize,
                     // false since we could have concurrent uses of the handle,
                     // when when reading the TIFF TileOffsets / TileByteCounts
                     // array
-                    std::lock_guard<std::mutex> oLock(sContext.oMutex);
+                    std::lock_guard<std::recursive_mutex> oLock(
+                        sContext.oMutex);
 
                     IsBlockAvailable(nBlockId, &asJobs[iJob].nOffset,
                                      &asJobs[iJob].nSize);
@@ -1314,7 +1321,8 @@ CPLErr GTiffDataset::MultiThreadedRead(int nXOff, int nYOff, int nXSize,
                 {
                     if (nFileSize == 0)
                     {
-                        std::lock_guard<std::mutex> oLock(sContext.oMutex);
+                        std::lock_guard<std::recursive_mutex> oLock(
+                            sContext.oMutex);
                         sContext.poHandle->Seek(0, SEEK_END);
                         nFileSize = sContext.poHandle->Tell();
                     }
@@ -1326,7 +1334,8 @@ CPLErr GTiffDataset::MultiThreadedRead(int nXOff, int nYOff, int nXSize,
                                  static_cast<GUIntBig>(asJobs[iJob].nSize),
                                  static_cast<GUIntBig>(asJobs[iJob].nOffset));
 
-                        std::lock_guard<std::mutex> oLock(sContext.oMutex);
+                        std::lock_guard<std::recursive_mutex> oLock(
+                            sContext.oMutex);
                         sContext.bSuccess = false;
                         break;
                     }
@@ -1377,6 +1386,48 @@ CPLErr GTiffDataset::MultiThreadedRead(int nXOff, int nYOff, int nXSize,
                         static_cast<size_t>(std::min<vsi_l_offset>(
                             std::numeric_limits<size_t>::max(),
                             asJobs[iJob].nSize));
+
+                    // If the total number of bytes we must read excess the
+                    // capacity of AdviseRead(), then split the RasterIO()
+                    // request in 2 halves.
+                    if (nAdviseReadTotalBytesLimit > 0 &&
+                        anSizes[nAdviseReadRanges] <
+                            nAdviseReadTotalBytesLimit &&
+                        anSizes[nAdviseReadRanges] >
+                            nAdviseReadTotalBytesLimit - nAdviseReadAccBytes &&
+                        nYBlocks >= 2)
+                    {
+                        const int nYOff2 =
+                            (nBlockYStart + nYBlocks / 2) * m_nBlockYSize;
+                        CPLDebugOnly("GTiff",
+                                     "Splitting request (%d,%d,%dx%d) into "
+                                     "(%d,%d,%dx%d) and (%d,%d,%dx%d)",
+                                     nXOff, nYOff, nXSize, nYSize, nXOff, nYOff,
+                                     nXSize, nYOff2 - nYOff, nXOff, nYOff2,
+                                     nXSize, nYOff + nYSize - nYOff2);
+
+                        asJobs.clear();
+                        anOffsets.clear();
+                        anSizes.clear();
+                        poQueue.reset();
+
+                        CPLErr eErr = MultiThreadedRead(
+                            nXOff, nYOff, nXSize, nYOff2 - nYOff, pData,
+                            eBufType, nBandCount, panBandMap, nPixelSpace,
+                            nLineSpace, nBandSpace);
+                        if (eErr == CE_None)
+                        {
+                            eErr = MultiThreadedRead(
+                                nXOff, nYOff2, nXSize, nYOff + nYSize - nYOff2,
+                                static_cast<GByte *>(pData) +
+                                    (nYOff2 - nYOff) * nLineSpace,
+                                eBufType, nBandCount, panBandMap, nPixelSpace,
+                                nLineSpace, nBandSpace);
+                        }
+                        return eErr;
+                    }
+                    nAdviseReadAccBytes += anSizes[nAdviseReadRanges];
+
                     ++nAdviseReadRanges;
                 }
 
diff --git a/port/cpl_vsi_virtual.h b/port/cpl_vsi_virtual.h
index e2458e37371e..225e2eded076 100644
--- a/port/cpl_vsi_virtual.h
+++ b/port/cpl_vsi_virtual.h
@@ -87,6 +87,23 @@ struct CPL_DLL VSIVirtualHandle
     {
     }
 
+    /** Return the total maximum number of bytes that AdviseRead() can handle
+     * at once.
+     *
+     * Some AdviseRead() implementations may give up if the sum of the values
+     * in the panSizes[] array provided to AdviseRead() exceeds a limit.
+     *
+     * Callers might use that threshold to optimize the efficiency of
+     * AdviseRead().
+     *
+     * A returned value of 0 indicates a unknown limit.
+     * @since GDAL 3.9
+     */
+    virtual size_t GetAdviseReadTotalBytesLimit() const
+    {
+        return 0;
+    }
+
     virtual size_t Write(const void *pBuffer, size_t nSize, size_t nCount) = 0;
 
     int Printf(CPL_FORMAT_STRING(const char *pszFormat), ...)
diff --git a/port/cpl_vsil_curl.cpp b/port/cpl_vsil_curl.cpp
index c8d6640a7100..38d6140529bb 100644
--- a/port/cpl_vsil_curl.cpp
+++ b/port/cpl_vsil_curl.cpp
@@ -32,9 +32,10 @@
 
 #include <algorithm>
 #include <array>
-#include <set>
+#include <limits>
 #include <map>
 #include <memory>
+#include <set>
 
 #include "cpl_aws.h"
 #include "cpl_json.h"
@@ -3153,6 +3154,21 @@ size_t VSICurlHandle::PRead(void *pBuffer, size_t nSize,
     return nRet;
 }
 
+/************************************************************************/
+/*                  GetAdviseReadTotalBytesLimit()                      */
+/************************************************************************/
+
+size_t VSICurlHandle::GetAdviseReadTotalBytesLimit() const
+{
+    return static_cast<size_t>(std::min<unsigned long long>(
+        std::numeric_limits<size_t>::max(),
+        // 100 MB
+        std::strtoull(
+            CPLGetConfigOption("CPL_VSIL_CURL_ADVISE_READ_TOTAL_BYTES_LIMIT",
+                               "104857600"),
+            nullptr, 10)));
+}
+
 /************************************************************************/
 /*                         AdviseRead()                                 */
 /************************************************************************/
@@ -3171,9 +3187,10 @@ void VSICurlHandle::AdviseRead(int nRanges, const vsi_l_offset *panOffsets,
 
     // Give up if we need to allocate too much memory
     vsi_l_offset nMaxSize = 0;
+    const size_t nLimit = GetAdviseReadTotalBytesLimit();
     for (int i = 0; i < nRanges; ++i)
     {
-        if (panSizes[i] > 100 * 1024 * 1024 - nMaxSize)
+        if (panSizes[i] > nLimit - nMaxSize)
         {
             CPLDebug(poFS->GetDebugKey(),
                      "Trying to request too many bytes in AdviseRead()");
@@ -3994,7 +4011,10 @@ const char *VSICurlFilesystemHandlerBase::GetActualURL(const char *pszFilename)
     "default='16384000'/>"                                                     \
     "  <Option name='CPL_VSIL_CURL_IGNORE_GLACIER_STORAGE' type='boolean' "    \
     "description='Whether to skip files with Glacier storage class in "        \
-    "directory listing.' default='YES'/>"
+    "directory listing.' default='YES'/>"                                      \
+    "  <Option name='CPL_VSIL_CURL_ADVISE_READ_TOTAL_BYTES_LIMIT' "            \
+    "type='integer' description='Maximum number of bytes AdviseRead() is "     \
+    "allowed to fetch at once' default='104857600'/>"
 
 const char *VSICurlFilesystemHandlerBase::GetOptionsStatic()
 {
diff --git a/port/cpl_vsil_curl_class.h b/port/cpl_vsil_curl_class.h
index 97d1e618a35a..853d579954db 100644
--- a/port/cpl_vsil_curl_class.h
+++ b/port/cpl_vsil_curl_class.h
@@ -506,6 +506,8 @@ class VSICurlHandle : public VSIVirtualHandle
     void AdviseRead(int nRanges, const vsi_l_offset *panOffsets,
                     const size_t *panSizes) override;
 
+    size_t GetAdviseReadTotalBytesLimit() const override;
+
     bool IsKnownFileSize() const
     {
         return oFileProp.bHasComputedFileSize;