diff --git a/NEWS.md b/NEWS.md
index e8e2464992..6ac423458e 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -7,7 +7,7 @@
 
 * Using testthat 3rd edition. 
 
-* Fixed bug introduced in `across()` in previous version (#5765).
+* Fixed bugs introduced in `across()` in previous version (#5765).
 
 * `group_by()` keeps attributes unrelated to the grouping (#5760).
 
diff --git a/R/mutate.R b/R/mutate.R
index 45c48e2bb0..aa82b80dae 100644
--- a/R/mutate.R
+++ b/R/mutate.R
@@ -236,7 +236,10 @@ mutate_cols <- function(.data, ...) {
     for (i in seq_along(dots)) {
       mask$across_cache_reset()
 
+      # get results from all the quosures that are expanded from ..i
+      # then ingest them after
       quosures <- expand_quosure(dots[[i]])
+      quosures_results <- vector(mode = "list", length = length(quosures))
 
       for (k in seq_along(quosures)) {
         quo <- quosures[[k]]
@@ -283,11 +286,6 @@ mutate_cols <- function(.data, ...) {
         }
 
         if (is.null(chunks)) {
-          if (quo_data$is_named) {
-            name <- quo_data$name_given
-            new_columns[[name]] <- zap()
-            mask$remove(name)
-          }
           next
         }
 
@@ -305,6 +303,27 @@ mutate_cols <- function(.data, ...) {
           }
         }
 
+        quosures_results[[k]] <- list(result = result, chunks = chunks)
+      }
+
+
+      for (k in seq_along(quosures)) {
+        quo <- quosures[[k]]
+        quo_data <- attr(quo, "dplyr:::data")
+
+        quo_result <- quosures_results[[k]]
+        if (is.null(quo_result)) {
+          if (quo_data$is_named) {
+            name <- quo_data$name_given
+            new_columns[[name]] <- zap()
+            mask$remove(name)
+          }
+          next
+        }
+
+        result <- quo_result$result
+        chunks <- quo_result$chunks
+
         if (!quo_data$is_named && is.data.frame(result)) {
           new_columns[names(result)] <- result
           mask$add_many(result, chunks)
diff --git a/R/summarise.R b/R/summarise.R
index 0e4f0bed70..157ae528c0 100644
--- a/R/summarise.R
+++ b/R/summarise.R
@@ -225,6 +225,7 @@ summarise_cols <- function(.data, ...) {
       mask$across_cache_reset()
 
       quosures <- expand_quosure(dots[[i]])
+      quosures_results <- vector(mode = "list", length = length(quosures))
 
       # with the previous part above, for each element of ... we can
       # have either one or several quosures, each of them handled here:
@@ -246,6 +247,20 @@ summarise_cols <- function(.data, ...) {
         )
         chunks_k <- vec_cast_common(!!!chunks_k, .to = types_k)
 
+        quosures_results[[k]] <- list(chunks = chunks_k, types = types_k)
+      }
+
+      for (k in seq_along(quosures)) {
+        quo <- quosures[[k]]
+        quo_data <- attr(quo, "dplyr:::data")
+
+        quo_result <- quosures_results[[k]]
+        if (is.null(quo_result)) {
+          next
+        }
+        types_k <- quo_result$types
+        chunks_k <- quo_result$chunks
+
         if (!quo_data$is_named && is.data.frame(types_k)) {
           chunks_extracted <- .Call(dplyr_extract_chunks, chunks_k, types_k)
 
diff --git a/tests/testthat/test-across.R b/tests/testthat/test-across.R
index 2bd0092da8..cf4fd61752 100644
--- a/tests/testthat/test-across.R
+++ b/tests/testthat/test-across.R
@@ -254,28 +254,88 @@ test_that("across() works with empty data frames (#5523)", {
    )
 })
 
-test_that("lambdas in across() can use columns", {
+test_that("lambdas in mutate() + across() can use columns", {
   df <- tibble(x = 2, y = 4, z = 8)
   expect_identical(
-    df %>% mutate_all(~ .x / y),
+    df %>% mutate(data.frame(x = x / y, y = y / y, z = z / y)),
     df %>% mutate(across(everything(), ~ .x / y))
   )
   expect_identical(
-    df %>% mutate_all(~ .x / y),
+    df %>% mutate(data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% mutate(+across(everything(), ~ .x / y))
+  )
+
+  expect_identical(
+    df %>% mutate(data.frame(x = x / y, y = y / y, z = z / y)),
     df %>% mutate(across(everything(), ~ .x / .data$y))
   )
+  expect_identical(
+    df %>% mutate(data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% mutate(+across(everything(), ~ .x / .data$y))
+  )
+})
+
+test_that("lambdas in summarise() + across() can use columns", {
+  df <- tibble(x = 2, y = 4, z = 8)
+  expect_identical(
+    df %>% summarise(data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% summarise(across(everything(), ~ .x / y))
+  )
+  expect_identical(
+    df %>% summarise(data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% summarise(+across(everything(), ~ .x / y))
+  )
+
+  expect_identical(
+    df %>% summarise(data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% summarise(across(everything(), ~ .x / .data$y))
+  )
+  expect_identical(
+    df %>% summarise(data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% summarise(+across(everything(), ~ .x / .data$y))
+  )
 })
 
-test_that("lambdas in across() can use columns in follow up expressions (#5717)", {
+test_that("lambdas in mutate() + across() can use columns in follow up expressions (#5717)", {
   df <- tibble(x = 2, y = 4, z = 8)
   expect_identical(
-    df %>% mutate(a = 2, x = x / y, y = y / y, z = z / y),
+    df %>% mutate(a = 2, data.frame(x = x / y, y = y / y, z = z / y)),
     df %>% mutate(a = 2, across(c(x, y, z), ~ .x / y))
   )
   expect_identical(
-    df %>% mutate(a = 2, x = x / y, y = y / y, z = z / y),
+    df %>% mutate(a = 2, data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% mutate(a = 2, +across(c(x, y, z), ~ .x / y))
+  )
+
+  expect_identical(
+    df %>% mutate(a = 2, data.frame(x = x / y, y = y / y, z = z / y)),
     df %>% mutate(a = 2, across(c(x, y, z), ~ .x / .data$y))
   )
+  expect_identical(
+    df %>% mutate(a = 2, data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% mutate(a = 2, +across(c(x, y, z), ~ .x / .data$y))
+  )
+})
+
+test_that("lambdas in summarise() + across() can use columns in follow up expressions (#5717)", {
+  df <- tibble(x = 2, y = 4, z = 8)
+  expect_identical(
+    df %>% summarise(a = 2, data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% summarise(a = 2, across(c(x, y, z), ~ .x / y))
+  )
+  expect_identical(
+    df %>% summarise(a = 2, data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% summarise(a = 2, +across(c(x, y, z), ~ .x / y))
+  )
+
+  expect_identical(
+    df %>% summarise(a = 2, data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% summarise(a = 2, across(c(x, y, z), ~ .x / .data$y))
+  )
+  expect_identical(
+    df %>% summarise(a = 2, data.frame(x = x / y, y = y / y, z = z / y)),
+    df %>% summarise(a = 2, +across(c(x, y, z), ~ .x / .data$y))
+  )
 })
 
 test_that("functions defined inline can use columns (#5734)", {