Hi liberty cabbage,
There is more information in the foundation post here and the posts it links to (in the second paragraph) about the types of support system that would be suitable for different types of mattresses but as a general rule (subject to any warranty criteria that are part of the manufacturer’s warranty) any foam mattress will be fine on a slatted platform or wire grid surface (although I would be cautious with a wire grid surface with a mattress that has a latex support core … see post #10 here).
Also as a very general rule … most pocket coil mattresses will also be fine and “some” other types of innerspring mattresses will be fine as well depending on the specifics of their construction and on what is under the innerspring that can act as a “shock absorber” but with innerspring mattresses I would always follow the recommendations of the manufacturer of the mattress you are considering.
Outside of the previous comments and suggestions … I would follow the same guidelines as I would for any other mattress and I would make sure you’ve read the mattress shopping tutorial here which has all the basic information, steps, and guidelines you will need to make the best possible choices regardless of which type of mattress or support system you are considering.
Phoenix