diff --git a/backend/union/entry.go b/backend/union/entry.go
index 1123183d8..efd2cbaef 100644
--- a/backend/union/entry.go
+++ b/backend/union/entry.go
@@ -4,6 +4,7 @@ import (
 	"context"
 	"fmt"
 	"io"
+	"io/ioutil"
 	"sync"
 	"time"
 
@@ -84,6 +85,10 @@ func (o *Object) Update(ctx context.Context, in io.Reader, src fs.ObjectInfo, op
 			err := o.Update(ctx, readers[i], src, options...)
 			if err != nil {
 				errs[i] = fmt.Errorf("%s: %w", o.UpstreamFs().Name(), err)
+				if len(entries) > 1 {
+					// Drain the input buffer to allow other uploads to continue
+					_, _ = io.Copy(ioutil.Discard, readers[i])
+				}
 			}
 		} else {
 			errs[i] = fs.ErrorNotAFile
diff --git a/backend/union/union.go b/backend/union/union.go
index 0b01bddce..46c697a64 100644
--- a/backend/union/union.go
+++ b/backend/union/union.go
@@ -6,6 +6,7 @@ import (
 	"errors"
 	"fmt"
 	"io"
+	"io/ioutil"
 	"path"
 	"path/filepath"
 	"strings"
@@ -486,6 +487,10 @@ func (f *Fs) put(ctx context.Context, in io.Reader, src fs.ObjectInfo, stream bo
 		}
 		if err != nil {
 			errs[i] = fmt.Errorf("%s: %w", u.Name(), err)
+			if len(upstreams) > 1 {
+				// Drain the input buffer to allow other uploads to continue
+				_, _ = io.Copy(ioutil.Discard, readers[i])
+			}
 			return
 		}
 		objs[i] = u.WrapObject(o)