diff --git a/backend/azureblob/azureblob.go b/backend/azureblob/azureblob.go
index 430b72778..c4fdb827a 100644
--- a/backend/azureblob/azureblob.go
+++ b/backend/azureblob/azureblob.go
@@ -343,6 +343,16 @@ In tests, copy speed increases almost linearly with copy
 concurrency.`,
 			Default:  512,
 			Advanced: true,
+		}, {
+			Name: "copy_total_concurrency",
+			Help: `Global concurrency limit for multipart copy chunks.
+
+This limits the total number of multipart copy chunks running at once
+across all files.
+
+Set to 0 to disable this limiter.`,
+			Default:  0,
+			Advanced: true,
 		}, {
 			Name: "use_copy_blob",
 			Help: `Whether to use the Copy Blob API when copying to the same storage account.
@@ -526,6 +536,7 @@ type Options struct {
 	ChunkSize                  fs.SizeSuffix        `config:"chunk_size"`
 	CopyCutoff                 fs.SizeSuffix        `config:"copy_cutoff"`
 	CopyConcurrency            int                  `config:"copy_concurrency"`
+	CopyTotalConcurrency       int                  `config:"copy_total_concurrency"`
 	UseCopyBlob                bool                 `config:"use_copy_blob"`
 	UploadConcurrency          int                  `config:"upload_concurrency"`
 	ListChunkSize              uint                 `config:"list_chunk"`
@@ -560,6 +571,7 @@ type Fs struct {
 	cache         *bucket.Cache                // cache for container creation status
 	pacer         *fs.Pacer                    // To pace and retry the API calls
 	uploadToken   *pacer.TokenDispenser        // control concurrency
+	copyToken     *pacer.TokenDispenser        // global multipart copy concurrency limiter
 	publicAccess  container.PublicAccessType   // Container Public Access Level
 
 	// user delegation cache
@@ -802,6 +814,7 @@ func NewFs(ctx context.Context, name, root string, m configmap.Mapper) (fs.Fs, e
 		ci:          ci,
 		pacer:       fs.NewPacer(ctx, pacer.NewS3(pacer.MinSleep(minSleep), pacer.MaxSleep(maxSleep), pacer.DecayConstant(decayConstant))),
 		uploadToken: pacer.NewTokenDispenser(ci.Transfers),
+		copyToken:   pacer.NewTokenDispenser(opt.CopyTotalConcurrency),
 		cache:       bucket.NewCache(),
 		cntSVCcache: make(map[string]*container.Client, 1),
 	}
@@ -1875,8 +1888,14 @@ func (f *Fs) copyMultipart(ctx context.Context, remote, dstContainer, dstPath st
 		if gCtx.Err() != nil {
 			break
 		}
+		if f.opt.CopyTotalConcurrency > 0 {
+			f.copyToken.Get()
+		}
 		partNum := partNum // for closure
 		g.Go(func() error {
+			if f.opt.CopyTotalConcurrency > 0 {
+				defer f.copyToken.Put()
+			}
 			blockID := bic.newBlockID(partNum)
 			options := blockblob.StageBlockFromURLOptions{
 				Range: blob.HTTPRange{