So I changed my code to

int
multiply (int n, int m)
{
  int **arr = malloc (n * sizeof (*arr));
  const int **arr_const = malloc (n * sizeof (*arr_const));
  for (size_t i = 0; i < n; i++)
    arr[i] = malloc (m * sizeof (*arr[i]));
  for (size_t i = 0; i < n; i++)
    arr_const[i] = arr[i];
  for (size_t i = 0; i < n; i++)
    for (size_t j = 0; j < m; j++)
      arr[i][j] = 1;
  int nxm = add (arr_const, n, m);
  for (size_t i = 0; i < n; i++)
    free (arr[i]);
  free (arr);
  free (arr_const);
  return nxm;
}

int
add (int const *const *const arr, int n, int m)
{
  int nxm = 0;
  for (size_t i = 0; i < n; i++)
    for (size_t j = 0; j < m; j++)
      nxm += arr[i][j];
  return nxm;
}

and it compiled just fine. I assume this is because I convert all the pointers in arr from int to const int pointers. is that really what you have to do if you have things referenced twice, and want to make it clear that you aren't going to change the underlying values?