To clarify, Fmoc-protected solid phase synthesis utilizes acid-cleavable side chain protecting groups (e.g. Boc, trityl, t-butyl) and Fmoc protection of the primary amine on the amino acid. The Fmoc group is base cleavable, but this only removes the N-terminal protection.
Most resins in Fmoc SPPS are acid cleavable as well, so that removal of the completed chain by resin also universally deprotects the side chains. If for some reason you want to keep the protecting groups on, you need a resin that's cleaved by neither acidic conditions or basic conditions.
I think there are some orthogonal resins out there, but they might be tricky to find. I seem to recall something about a light-cleavable resin at one point.