diff --git a/R/compute_vS.R b/R/compute_vS.R
index 321a391d3..6c3b26f19 100644
--- a/R/compute_vS.R
+++ b/R/compute_vS.R
@@ -231,6 +231,7 @@ compute_MCint <- function(dt, pred_cols = "p_hat") {
 #' @keywords internal
 append_vS_list <- function(vS_list, internal) {
   iter <- length(internal$iter_list)
+  keep_samp_for_vS <- internal$parameters$output_args$keep_samp_for_vS
 
   # Adds v_S output above to any vS_list already computed
   if (iter > 1) {
@@ -249,17 +250,53 @@ append_vS_list <- function(vS_list, internal) {
     prev_vS_list_new <- list()
 
     # Applies the mapper to update the prev_vS_list ot the new id_coalition numbering
-    for (k in seq_along(prev_vS_list)) {
-      prev_vS_list_new[[k]] <- merge(prev_vS_list[[k]],
-        id_coalitions_mapper[, .(id_coalition, id_coalition_new)],
-        by = "id_coalition"
-      )
-      prev_vS_list_new[[k]][, id_coalition := id_coalition_new]
-      prev_vS_list_new[[k]][, id_coalition_new := NULL]
+    if (isFALSE(keep_samp_for_vS)) {
+      for (k in seq_along(prev_vS_list)) {
+        this_vS <- prev_vS_list[[k]]
+
+        this_vS_new <- merge(this_vS,
+          id_coalitions_mapper[, .(id_coalition, id_coalition_new)],
+          by = "id_coalition"
+        )
+
+        this_vS_new[, id_coalition := id_coalition_new]
+        this_vS_new[, id_coalition_new := NULL]
+
+
+        prev_vS_list_new[[k]] <- this_vS_new
+      }
+    } else {
+      for (k in seq_along(prev_vS_list)) {
+        this_vS <- prev_vS_list[[k]]$dt_vS
+        this_samp_for_vS <- prev_vS_list[[k]]$dt_samp_for_vS
+
+
+        this_vS_new <- merge(this_vS,
+          id_coalitions_mapper[, .(id_coalition, id_coalition_new)],
+          by = "id_coalition"
+        )
+
+        this_vS_new[, id_coalition := id_coalition_new]
+        this_vS_new[, id_coalition_new := NULL]
+
+        this_samp_for_vS_new <- merge(this_samp_for_vS,
+          id_coalitions_mapper[, .(id_coalition, id_coalition_new)],
+          by = "id_coalition"
+        )
+
+        this_samp_for_vS_new[, id_coalition := id_coalition_new]
+        this_samp_for_vS_new[, id_coalition_new := NULL]
+
+
+        prev_vS_list_new[[k]] <- list(dt_vS = this_vS_new, dt_samp_for_vS = this_samp_for_vS_new)
+      }
     }
+    names(prev_vS_list_new) <- names(prev_vS_list)
 
     # Merge the new vS_list with the old vS_list
     vS_list <- c(prev_vS_list_new, vS_list)
   }
+
+
   return(vS_list)
 }
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diff --git a/tests/testthat/_snaps/asymmetric-causal-output/output_mixed_sym_caus_conf_TRUE_iterative.rds b/tests/testthat/_snaps/asymmetric-causal-output/output_mixed_sym_caus_conf_TRUE_iterative.rds
index dca60b54b..f57d561a5 100644
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diff --git a/tests/testthat/_snaps/adaptive-output.md b/tests/testthat/_snaps/iterative-output.md
similarity index 96%
rename from tests/testthat/_snaps/adaptive-output.md
rename to tests/testthat/_snaps/iterative-output.md
index 72239e8d0..c3c2d8622 100644
--- a/tests/testthat/_snaps/adaptive-output.md
+++ b/tests/testthat/_snaps/iterative-output.md
@@ -982,3 +982,38 @@
       2:          2 42.44   4.919  -4.878 -11.9086 -0.8405 -1.1714
       3:          3 42.44   7.447 -25.748   0.0324 -0.1976  0.8978
 
+# output_lm_numeric_independence_keep_samp_for_vS
+
+    Code
+      (out <- code)
+    Message
+      Success with message:
+      max_n_coalitions is NULL or larger than or 2^n_features = 32, 
+      and is therefore set to 2^n_features = 32.
+      
+      * Model class: <lm>
+      * Approach: independence
+      * Iterative estimation: TRUE
+      * Number of feature-wise Shapley values: 5
+      * Number of observations to explain: 3
+      
+      -- iterative computation started --
+      
+      -- Iteration 1 -----------------------------------------------------------------
+      i Using 5 of 32 coalitions, 5 new. 
+      
+      -- Iteration 2 -----------------------------------------------------------------
+      i Using 10 of 32 coalitions, 4 new. 
+      
+      -- Iteration 3 -----------------------------------------------------------------
+      i Using 12 of 32 coalitions, 2 new. 
+      
+      -- Iteration 4 -----------------------------------------------------------------
+      i Using 16 of 32 coalitions, 4 new. 
+    Output
+         explain_id  none Solar.R    Wind   Temp  Month    Day
+              <int> <num>   <num>   <num>  <num>  <num>  <num>
+      1:          1 42.44  -4.541   8.330 17.491 -5.585 -3.093
+      2:          2 42.44   2.246  -3.285 -5.258 -5.585 -1.997
+      3:          3 42.44   3.704 -18.549 -1.467 -2.545  1.289
+
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diff --git a/tests/testthat/_snaps/adaptive-setup.md b/tests/testthat/_snaps/iterative-setup.md
similarity index 100%
rename from tests/testthat/_snaps/adaptive-setup.md
rename to tests/testthat/_snaps/iterative-setup.md
diff --git a/tests/testthat/_snaps/regression-output/output_lm_numeric_lm_separate_iterative.rds b/tests/testthat/_snaps/regression-output/output_lm_numeric_lm_separate_iterative.rds
index c2ff52301..abe999492 100644
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diff --git a/tests/testthat/test-adaptive-output.R b/tests/testthat/test-iterative-output.R
similarity index 93%
rename from tests/testthat/test-adaptive-output.R
rename to tests/testthat/test-iterative-output.R
index 0be8006c0..1974ecb64 100644
--- a/tests/testthat/test-adaptive-output.R
+++ b/tests/testthat/test-iterative-output.R
@@ -310,3 +310,23 @@ test_that("output_verbose_1_3_4_5", {
     "output_verbose_1_3_4_5"
   )
 })
+
+
+# Just checking that internal$output$dt_samp_for_vS  works for iterative
+test_that("output_lm_numeric_independence_keep_samp_for_vS", {
+  expect_snapshot_rds(
+    (out <- explain(
+      testing = TRUE,
+      model = model_lm_numeric,
+      x_explain = x_explain_numeric,
+      x_train = x_train_numeric,
+      approach = "independence",
+      phi0 = p0,
+      output_args = list(keep_samp_for_vS = TRUE),
+      iterative = TRUE
+    )),
+    "output_lm_numeric_independence_keep_samp_for_vS"
+  )
+
+  expect_false(is.null(out$internal$output$dt_samp_for_vS))
+})
diff --git a/tests/testthat/test-adaptive-setup.R b/tests/testthat/test-iterative-setup.R
similarity index 100%
rename from tests/testthat/test-adaptive-setup.R
rename to tests/testthat/test-iterative-setup.R