diff --git a/pkg/store/acceptance_test.go b/pkg/store/acceptance_test.go
index fcf93073a3..26d6523f30 100644
--- a/pkg/store/acceptance_test.go
+++ b/pkg/store/acceptance_test.go
@@ -999,43 +999,140 @@ func TestTSDBStore_Acceptance(t *testing.T) {
 }
 
 func TestProxyStoreWithTSDBSelector_Acceptance(t *testing.T) {
+	t.Skip("This is a known issue, we need to think how to fix it")
+
 	t.Cleanup(func() { custom.TolerantVerifyLeak(t) })
+	ctx := context.Background()
 
 	startStore := func(tt *testing.T, extLset labels.Labels, appendFn func(app storage.Appender)) storepb.StoreServer {
-		startNestedStore := func(tt *testing.T, extLset labels.Labels, appendFn func(app storage.Appender)) storepb.StoreServer {
-			db, err := e2eutil.NewTSDB()
+		startNestedStore := func(tt *testing.T, appendFn func(app storage.Appender), extLsets ...labels.Labels) storepb.StoreServer {
+			tmpDir := tt.TempDir()
+			bktDir := filepath.Join(tmpDir, "bkt")
+			auxDir := filepath.Join(tmpDir, "aux")
+			metaDir := filepath.Join(tmpDir, "meta")
+
+			testutil.Ok(tt, os.MkdirAll(metaDir, os.ModePerm))
+			testutil.Ok(tt, os.MkdirAll(auxDir, os.ModePerm))
+
+			bkt, err := filesystem.NewBucket(bktDir)
 			testutil.Ok(tt, err)
-			tt.Cleanup(func() { testutil.Ok(tt, db.Close()) })
-			appendFn(db.Appender(context.Background()))
+			tt.Cleanup(func() { testutil.Ok(tt, bkt.Close()) })
 
-			return NewTSDBStore(nil, db, component.Rule, extLset)
+			headOpts := tsdb.DefaultHeadOptions()
+			headOpts.ChunkDirRoot = tmpDir
+			headOpts.ChunkRange = 1000
+			h, err := tsdb.NewHead(nil, nil, nil, nil, headOpts, nil)
+			testutil.Ok(tt, err)
+			tt.Cleanup(func() { testutil.Ok(tt, h.Close()) })
+			logger := log.NewNopLogger()
+
+			appendFn(h.Appender(context.Background()))
+
+			if h.NumSeries() == 0 {
+				tt.Skip("Bucket Store cannot handle empty HEAD")
+			}
+
+			for _, extLset := range extLsets {
+				id := createBlockFromHead(tt, auxDir, h)
+
+				auxBlockDir := filepath.Join(auxDir, id.String())
+				meta, err := metadata.ReadFromDir(auxBlockDir)
+				testutil.Ok(t, err)
+				stats, err := block.GatherIndexHealthStats(ctx, logger, filepath.Join(auxBlockDir, block.IndexFilename), meta.MinTime, meta.MaxTime)
+				testutil.Ok(t, err)
+				_, err = metadata.InjectThanos(log.NewNopLogger(), auxBlockDir, metadata.Thanos{
+					Labels:     extLset.Map(),
+					Downsample: metadata.ThanosDownsample{Resolution: 0},
+					Source:     metadata.TestSource,
+					IndexStats: metadata.IndexStats{SeriesMaxSize: stats.SeriesMaxSize, ChunkMaxSize: stats.ChunkMaxSize},
+				}, nil)
+				testutil.Ok(tt, err)
+
+				testutil.Ok(tt, block.Upload(ctx, logger, bkt, auxBlockDir, metadata.NoneFunc))
+			}
 
+			chunkPool, err := NewDefaultChunkBytesPool(2e5)
+			testutil.Ok(tt, err)
+
+			insBkt := objstore.WithNoopInstr(bkt)
+			baseBlockIDsFetcher := block.NewConcurrentLister(logger, insBkt)
+			metaFetcher, err := block.NewMetaFetcher(logger, 20, insBkt, baseBlockIDsFetcher, metaDir, nil, []block.MetadataFilter{
+				block.NewTimePartitionMetaFilter(allowAllFilterConf.MinTime, allowAllFilterConf.MaxTime),
+			})
+			testutil.Ok(tt, err)
+
+			bucketStore, err := NewBucketStore(
+				objstore.WithNoopInstr(bkt),
+				metaFetcher,
+				"",
+				NewChunksLimiterFactory(10e6),
+				NewSeriesLimiterFactory(10e6),
+				NewBytesLimiterFactory(10e6),
+				NewGapBasedPartitioner(PartitionerMaxGapSize),
+				20,
+				true,
+				DefaultPostingOffsetInMemorySampling,
+				false,
+				false,
+				1*time.Minute,
+				WithChunkPool(chunkPool),
+				WithFilterConfig(allowAllFilterConf),
+			)
+			testutil.Ok(tt, err)
+			tt.Cleanup(func() { testutil.Ok(tt, bucketStore.Close()) })
+
+			testutil.Ok(tt, bucketStore.SyncBlocks(context.Background()))
+
+			return bucketStore
 		}
 
-		extLset1 := labels.NewBuilder(extLset).Set("replica", "A").Labels()
-		extLset2 := labels.NewBuilder(extLset).Set("replica", "B").Labels()
-		extLset3 := labels.NewBuilder(extLset).Set("replica", "C").Labels()
+		extLset1 := labels.NewBuilder(extLset).Set("L1", "A").Set("L2", "B").Labels()
+		extLset2 := labels.NewBuilder(extLset).Set("L1", "C").Set("L2", "D").Labels()
+		extLset3 := labels.NewBuilder(extLset).Set("L1", "A").Set("L2", "D").Labels()
 
-		p1 := startNestedStore(tt, extLset1, appendFn)
-		p2 := startNestedStore(tt, extLset2, appendFn)
-		p3 := startNestedStore(tt, extLset3, appendFn)
+		p1 := startNestedStore(tt, appendFn, extLset1, extLset2, extLset3)
 
 		clients := []Client{
-			storetestutil.TestClient{StoreClient: storepb.ServerAsClient(p1), ExtLset: []labels.Labels{extLset1}},
-			storetestutil.TestClient{StoreClient: storepb.ServerAsClient(p2), ExtLset: []labels.Labels{extLset2}},
-			storetestutil.TestClient{StoreClient: storepb.ServerAsClient(p3), ExtLset: []labels.Labels{extLset3}},
+			storetestutil.TestClient{StoreClient: storepb.ServerAsClient(p1), ExtLset: []labels.Labels{extLset1, extLset2, extLset3}},
 		}
 
 		relabelCfgs := []*relabel.Config{{
-			SourceLabels: model.LabelNames([]model.LabelName{"replica"}),
-			Regex:        relabel.MustNewRegexp("(A|C)"),
+			SourceLabels: model.LabelNames([]model.LabelName{"L1", "L2"}),
+			Separator:    "-",
+			Regex:        relabel.MustNewRegexp("(A-B|C-D)"),
 			Action:       relabel.Keep,
 		}}
 
 		return NewProxyStore(nil, nil, func() []Client { return clients }, component.Query, labels.EmptyLabels(), 0*time.Second, RetrievalStrategy(EagerRetrieval), WithTSDBSelector(NewTSDBSelector(relabelCfgs)))
 	}
 
-	testStoreAPIsAcceptance(t, startStore)
+	client := startStore(t, labels.EmptyLabels(), func(app storage.Appender) {
+		_, err := app.Append(0, labels.FromStrings("a", "b"), 0, 0)
+		testutil.Ok(t, err)
+		testutil.Ok(t, app.Commit())
+	})
+	srv := newStoreSeriesServer(ctx)
+
+	testutil.Ok(t, client.Series(&storepb.SeriesRequest{
+		MinTime: minTime.Unix(),
+		MaxTime: maxTime.Unix(),
+		Matchers: []storepb.LabelMatcher{
+			{Type: storepb.LabelMatcher_EQ, Name: "a", Value: "b"},
+		},
+	}, srv))
+
+	receivedLabels := make([]labels.Labels, 0)
+	for _, s := range srv.SeriesSet {
+		receivedLabels = append(receivedLabels, s.PromLabels())
+	}
+
+	// This fails currently because the method of using matchers cannot drop extLset3 even though we should only
+	// select extLset1 and extLset2 because of the TSDB Selector
+	testutil.Equals(t, receivedLabels, []labels.Labels{
+		labels.FromStrings("L1", "A", "L2", "B", "a", "b"),
+		labels.FromStrings("L1", "C", "L2", "D", "a", "b"),
+	})
+
 }
 
 func TestProxyStoreWithReplicas_Acceptance(t *testing.T) {