diff --git a/src/middle/Stan_math_signatures.ml b/src/middle/Stan_math_signatures.ml
index 2c10eb52c6..4abec7b8b1 100644
--- a/src/middle/Stan_math_signatures.ml
+++ b/src/middle/Stan_math_signatures.ml
@@ -1688,6 +1688,16 @@ let () =
     , ReturnType UReal
     , [UVector; UMatrix; UVector; UVector; UReal]
     , AoS ) ;
+  add_unqualified
+    ( "normal_id_glm_lpdf"
+    , ReturnType UReal
+    , [UReal; UMatrix; UReal; UVector; UReal]
+    , AoS ) ;
+  add_unqualified
+    ( "normal_id_glm_lpdf"
+    , ReturnType UReal
+    , [UReal; UMatrix; UVector; UVector; UReal]
+    , AoS ) ;
   add_unqualified
     ( "normal_id_glm_lpdf"
     , ReturnType UReal
@@ -1703,11 +1713,21 @@ let () =
     , ReturnType UReal
     , [UVector; URowVector; UReal; UVector; UVector]
     , AoS ) ;
+  add_unqualified
+    ( "normal_id_glm_lpdf"
+    , ReturnType UReal
+    , [UVector; URowVector; UVector; UVector; UReal]
+    , AoS ) ;
   add_unqualified
     ( "normal_id_glm_lpdf"
     , ReturnType UReal
     , [UVector; URowVector; UVector; UVector; UVector]
     , AoS ) ;
+  add_unqualified
+    ( "normal_id_glm_lpdf"
+    , ReturnType UReal
+    , [UVector; URowVector; UReal; UVector; UReal]
+    , AoS ) ;
   add_nullary "not_a_number" ;
   add_unqualified ("num_elements", ReturnType UInt, [UMatrix], AoS) ;
   add_unqualified ("num_elements", ReturnType UInt, [UVector], AoS) ;
diff --git a/test/integration/good/function-signatures/distributions/univariate/continuous/normal/normal_id_glm.stan b/test/integration/good/function-signatures/distributions/univariate/continuous/normal/normal_id_glm.stan
index 37a8cfadab..223b1d0a29 100644
--- a/test/integration/good/function-signatures/distributions/univariate/continuous/normal/normal_id_glm.stan
+++ b/test/integration/good/function-signatures/distributions/univariate/continuous/normal/normal_id_glm.stan
@@ -15,8 +15,12 @@ transformed data {
   transformed_data_real = normal_id_glm_lpdf(d_y_v| d_x_m, d_alpha_v, d_beta_v, d_phi);
   transformed_data_real = normal_id_glm_lpdf(d_y| d_x_m, d_alpha, d_beta_v, d_phi_v);
   transformed_data_real = normal_id_glm_lpdf(d_y| d_x_m, d_alpha_v, d_beta_v, d_phi_v);
+  transformed_data_real = normal_id_glm_lpdf(d_y| d_x_m, d_alpha, d_beta_v, d_phi);
+  transformed_data_real = normal_id_glm_lpdf(d_y| d_x_m, d_alpha_v, d_beta_v, d_phi);
   transformed_data_real = normal_id_glm_lpdf(d_y_v| d_x_rv, d_alpha, d_beta_v, d_phi_v);
   transformed_data_real = normal_id_glm_lpdf(d_y_v| d_x_rv, d_alpha_v, d_beta_v, d_phi_v);
+  transformed_data_real = normal_id_glm_lpdf(d_y_v| d_x_rv, d_alpha, d_beta_v, d_phi);
+  transformed_data_real = normal_id_glm_lpdf(d_y_v| d_x_rv, d_alpha_v, d_beta_v, d_phi);
 }
 parameters {
   real p_y;
@@ -36,10 +40,13 @@ transformed parameters {
   transformed_param_real = normal_id_glm_lpdf(p_y_v| p_x_m, p_alpha_v, p_beta_v, p_phi);
   transformed_param_real = normal_id_glm_lpdf(p_y| p_x_m, p_alpha, p_beta_v, p_phi_v);
   transformed_param_real = normal_id_glm_lpdf(p_y| p_x_m, p_alpha_v, p_beta_v, p_phi_v);
+  transformed_param_real = normal_id_glm_lpdf(p_y| p_x_m, p_alpha_v, p_beta_v, p_phi);
+  transformed_param_real = normal_id_glm_lpdf(p_y| p_x_m, p_alpha, p_beta_v, p_phi);
   transformed_param_real = normal_id_glm_lpdf(p_y_v| p_x_rv, p_alpha, p_beta_v, p_phi_v);
   transformed_param_real = normal_id_glm_lpdf(p_y_v| p_x_rv, p_alpha_v, p_beta_v, p_phi_v);
+  transformed_param_real = normal_id_glm_lpdf(p_y_v| p_x_rv, p_alpha, p_beta_v, p_phi);
+  transformed_param_real = normal_id_glm_lpdf(p_y_v| p_x_rv, p_alpha_v, p_beta_v, p_phi);
 }
 model {
   y_p ~ normal(0, 1);
 }
-
diff --git a/test/integration/good/function-signatures/distributions/univariate/continuous/normal/pretty.expected b/test/integration/good/function-signatures/distributions/univariate/continuous/normal/pretty.expected
index 84e807f7e8..2bfb559c1f 100644
--- a/test/integration/good/function-signatures/distributions/univariate/continuous/normal/pretty.expected
+++ b/test/integration/good/function-signatures/distributions/univariate/continuous/normal/pretty.expected
@@ -896,8 +896,12 @@ transformed data {
   transformed_data_real = normal_id_glm_lpdf(d_y_v | d_x_m, d_alpha_v, d_beta_v, d_phi);
   transformed_data_real = normal_id_glm_lpdf(d_y | d_x_m, d_alpha, d_beta_v, d_phi_v);
   transformed_data_real = normal_id_glm_lpdf(d_y | d_x_m, d_alpha_v, d_beta_v, d_phi_v);
+  transformed_data_real = normal_id_glm_lpdf(d_y | d_x_m, d_alpha, d_beta_v, d_phi);
+  transformed_data_real = normal_id_glm_lpdf(d_y | d_x_m, d_alpha_v, d_beta_v, d_phi);
   transformed_data_real = normal_id_glm_lpdf(d_y_v | d_x_rv, d_alpha, d_beta_v, d_phi_v);
   transformed_data_real = normal_id_glm_lpdf(d_y_v | d_x_rv, d_alpha_v, d_beta_v, d_phi_v);
+  transformed_data_real = normal_id_glm_lpdf(d_y_v | d_x_rv, d_alpha, d_beta_v, d_phi);
+  transformed_data_real = normal_id_glm_lpdf(d_y_v | d_x_rv, d_alpha_v, d_beta_v, d_phi);
 }
 parameters {
   real p_y;
@@ -917,8 +921,12 @@ transformed parameters {
   transformed_param_real = normal_id_glm_lpdf(p_y_v | p_x_m, p_alpha_v, p_beta_v, p_phi);
   transformed_param_real = normal_id_glm_lpdf(p_y | p_x_m, p_alpha, p_beta_v, p_phi_v);
   transformed_param_real = normal_id_glm_lpdf(p_y | p_x_m, p_alpha_v, p_beta_v, p_phi_v);
+  transformed_param_real = normal_id_glm_lpdf(p_y | p_x_m, p_alpha_v, p_beta_v, p_phi);
+  transformed_param_real = normal_id_glm_lpdf(p_y | p_x_m, p_alpha, p_beta_v, p_phi);
   transformed_param_real = normal_id_glm_lpdf(p_y_v | p_x_rv, p_alpha, p_beta_v, p_phi_v);
   transformed_param_real = normal_id_glm_lpdf(p_y_v | p_x_rv, p_alpha_v, p_beta_v, p_phi_v);
+  transformed_param_real = normal_id_glm_lpdf(p_y_v | p_x_rv, p_alpha, p_beta_v, p_phi);
+  transformed_param_real = normal_id_glm_lpdf(p_y_v | p_x_rv, p_alpha_v, p_beta_v, p_phi);
 }
 model {
   y_p ~ normal(0, 1);
diff --git a/test/integration/signatures/stan_math_signatures.t b/test/integration/signatures/stan_math_signatures.t
index d1b6f5e081..ca09b56951 100644
--- a/test/integration/signatures/stan_math_signatures.t
+++ b/test/integration/signatures/stan_math_signatures.t
@@ -15284,9 +15284,13 @@ Display all Stan math signatures exposed in the language
   normal_cdf_log(array[] real, array[] real, vector) => real
   normal_cdf_log(array[] real, array[] real, row_vector) => real
   normal_cdf_log(array[] real, array[] real, array[] real) => real
+  normal_id_glm_lpdf(real, matrix, real, vector, real) => real
   normal_id_glm_lpdf(real, matrix, real, vector, vector) => real
+  normal_id_glm_lpdf(real, matrix, vector, vector, real) => real
   normal_id_glm_lpdf(real, matrix, vector, vector, vector) => real
+  normal_id_glm_lpdf(vector, row_vector, real, vector, real) => real
   normal_id_glm_lpdf(vector, row_vector, real, vector, vector) => real
+  normal_id_glm_lpdf(vector, row_vector, vector, vector, real) => real
   normal_id_glm_lpdf(vector, row_vector, vector, vector, vector) => real
   normal_id_glm_lpdf(vector, matrix, real, vector, real) => real
   normal_id_glm_lpdf(vector, matrix, vector, vector, real) => real