By default, the functionality starts with and returns an additive BFV (RLWE) ciphertext, which does not support multiplications. To support multiplications, you should not perform the final homomorphic decoding in CKKS and remain in CKKS. Since the multiprecision sign evaluation performs iterative LUT evaluations, you should modify the last iteration to prevent decoding but keep in mind the scaling. Please see 1, 2 for some examples of performing leveled computations after FBT.
Alternatively, a simpler (you don’t modify the loop) but more expensive option is to take the RLWE output of the multiprecision sign evaluation, then perform an EvalFBTNoDecoding with the identity function.