diff --git a/CHANGELOG.md b/CHANGELOG.md
index 281386256..6ed434da5 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -34,6 +34,7 @@ Changelog for FrostFS Node
 - Parameters `nns-name` and `nns-zone` for command `frostfs-cli container create` (#37)
 - Tree service now saves the last synchronization height which persists across restarts (#82)
 - Add tracing support (#135)
+- Multiple (and a fix for single) copies number support for `PUT` requests (#221)
 
 ### Changed
 - Change `frostfs_node_engine_container_size` to counting sizes of logical objects
diff --git a/pkg/services/object/put/prm.go b/pkg/services/object/put/prm.go
index 27d9c9c7a..c8d1b29a2 100644
--- a/pkg/services/object/put/prm.go
+++ b/pkg/services/object/put/prm.go
@@ -42,6 +42,14 @@ func (p *PutInitPrm) WithObject(v *object.Object) *PutInitPrm {
 	return p
 }
 
+func (p *PutInitPrm) WithCopyNumbers(v []uint32) *PutInitPrm {
+	if p != nil && len(v) > 0 {
+		p.traverseOpts = append(p.traverseOpts, placement.WithCopyNumbers(v))
+	}
+
+	return p
+}
+
 func (p *PutInitPrm) WithRelay(f func(context.Context, client.NodeInfo, client.MultiAddressClient) error) *PutInitPrm {
 	if p != nil {
 		p.relay = f
diff --git a/pkg/services/object/put/v2/util.go b/pkg/services/object/put/v2/util.go
index 790f061f1..758470f6c 100644
--- a/pkg/services/object/put/v2/util.go
+++ b/pkg/services/object/put/v2/util.go
@@ -24,7 +24,8 @@ func (s *streamer) toInitPrm(part *objectV2.PutObjectPartInit, req *objectV2.Put
 			object.NewFromV2(oV2),
 		).
 		WithRelay(s.relayRequest).
-		WithCommonPrm(commonPrm), nil
+		WithCommonPrm(commonPrm).
+		WithCopyNumbers(part.GetCopiesNumber()), nil
 }
 
 func toChunkPrm(req *objectV2.PutObjectPartChunk) *putsvc.PutChunkPrm {
diff --git a/pkg/services/object_manager/placement/traverser.go b/pkg/services/object_manager/placement/traverser.go
index 75d5fbfd1..e46240a86 100644
--- a/pkg/services/object_manager/placement/traverser.go
+++ b/pkg/services/object_manager/placement/traverser.go
@@ -38,6 +38,7 @@ type Traverser struct {
 
 type cfg struct {
 	trackCopies bool
+	copyNumbers []uint32
 
 	flatSuccess *uint32
 
@@ -84,19 +85,23 @@ func NewTraverser(opts ...Option) (*Traverser, error) {
 		return nil, fmt.Errorf("could not build placement: %w", err)
 	}
 
+	// backward compatibility for scalar `copies_number`
+	if len(cfg.copyNumbers) == 1 {
+		cfg.flatSuccess = &cfg.copyNumbers[0]
+	}
+
 	var rem []int
 	if cfg.flatSuccess != nil {
 		ns = flatNodes(ns)
 		rem = []int{int(*cfg.flatSuccess)}
 	} else {
-		replNum := cfg.policy.NumberOfReplicas()
-		rem = make([]int, 0, replNum)
+		rem = defaultCopiesVector(cfg.policy)
 
-		for i := 0; i < replNum; i++ {
-			if cfg.trackCopies {
-				rem = append(rem, int(cfg.policy.ReplicaNumberByIndex(i)))
-			} else {
-				rem = append(rem, -1)
+		for i := range rem {
+			if !cfg.trackCopies {
+				rem[i] = -1
+			} else if len(cfg.copyNumbers) > i {
+				rem[i] = int(cfg.copyNumbers[i])
 			}
 		}
 	}
@@ -108,6 +113,17 @@ func NewTraverser(opts ...Option) (*Traverser, error) {
 	}, nil
 }
 
+func defaultCopiesVector(policy netmap.PlacementPolicy) []int {
+	replNum := policy.NumberOfReplicas()
+	copyVector := make([]int, 0, replNum)
+
+	for i := 0; i < replNum; i++ {
+		copyVector = append(copyVector, int(policy.ReplicaNumberByIndex(i)))
+	}
+
+	return copyVector
+}
+
 func flatNodes(ns [][]netmap.NodeInfo) [][]netmap.NodeInfo {
 	sz := 0
 	for i := range ns {
@@ -265,3 +281,9 @@ func WithoutSuccessTracking() Option {
 		c.trackCopies = false
 	}
 }
+
+func WithCopyNumbers(v []uint32) Option {
+	return func(c *cfg) {
+		c.copyNumbers = v
+	}
+}