I just found it in my notes. I don't think it looks too bad - everything you were going to do in the recursive part, you just do inside the subquery instead.

  WITH RECURSIVE my_cte AS (
    SELECT foo, bar FROM whatever
    UNION ALL
    SELECT (s).*
    FROM my_cte, LATERAL (
      SELECT ... -- refer to my_cte multiple times here
    ) s
  )