My apologies. I didn't read the documentation carefully enough. Note that it says that forms are pure functions that are applied to an association of previous input. So just define the subsequent forms explicitly as pure functions.
Here are some simple examples:
FormFunction[{{"x" -> "Number"}, {"y" -> {#x , 2, 3} } &}, {#x, #y} &][]
and
FormFunction[{{"x" -> {"cat", "actress"}}, {Switch[#x, "cat",
"y" -> "CatBreed", "actress",
"y" -> {Entity["Person", "AnneHathaway::fkdf7"],
Entity["Person", "HalleBerry::hj23z"],
Entity["Person", "LeeMeriwether::863fn"]}]} &}, #y["Image"] &, "PNG"]