diff --git a/src/core/proj/qgscoordinatetransform.cpp b/src/core/proj/qgscoordinatetransform.cpp
index 2304181cc5c4..cd934cb3f753 100644
--- a/src/core/proj/qgscoordinatetransform.cpp
+++ b/src/core/proj/qgscoordinatetransform.cpp
@@ -676,9 +676,27 @@ QgsRectangle QgsCoordinateTransform::transformBoundingBox( const QgsRectangle &r
   proj_errno_reset( projData );
   // proj documentation recommends 21 points for densification
   constexpr int DENSIFY_POINTS = 21;
-  const int projResult = proj_trans_bounds( projContext, projData, ( direction == Qgis::TransformDirection::Forward && !d->mIsReversed ) || ( direction == Qgis::TransformDirection::Reverse && d->mIsReversed ) ? PJ_FWD : PJ_INV,
-                         xMin, yMin, xMax, yMax,
-                         &transXMin, &transYMin, &transXMax, &transYMax, DENSIFY_POINTS );
+  int projResult = proj_trans_bounds( projContext, projData, ( direction == Qgis::TransformDirection::Forward && !d->mIsReversed ) || ( direction == Qgis::TransformDirection::Reverse && d->mIsReversed ) ? PJ_FWD : PJ_INV,
+                                      xMin, yMin, xMax, yMax,
+                                      &transXMin, &transYMin, &transXMax, &transYMax, DENSIFY_POINTS );
+
+  if ( ( projResult != 1
+         || !std::isfinite( transXMin )
+         || !std::isfinite( transXMax )
+         || !std::isfinite( transYMin )
+         || !std::isfinite( transYMax ) )
+       && ( d->mAvailableOpCount > 1 || d->mAvailableOpCount == -1 ) // only use fallbacks if more than one operation is possible -- otherwise we've already tried it and it failed
+     )
+  {
+    // fail #1 -- try with getting proj to auto-pick an appropriate coordinate operation for the points
+    if ( PJ *transform = d->threadLocalFallbackProjData() )
+    {
+      projResult = proj_trans_bounds( projContext, transform, ( direction == Qgis::TransformDirection::Forward && !d->mIsReversed ) || ( direction == Qgis::TransformDirection::Reverse && d->mIsReversed ) ? PJ_FWD : PJ_INV,
+                                      xMin, yMin, xMax, yMax,
+                                      &transXMin, &transYMin, &transXMax, &transYMax, DENSIFY_POINTS );
+    }
+  }
+
   if ( projResult != 1
        || !std::isfinite( transXMin )
        || !std::isfinite( transXMax )