Multi-signatures allow to combine several individual signatures into a compact one and verify it against a short aggregated key. Compared to threshold signatures, multi-signatures enjoy non-interactive key generation but give up on the threshold-setting. Recent works by Das et al. (CCS’23) and Garg et al. (S&P’24) show how multi-signatures can be turned into schemes that enable efficient verification when an ad hoc threshold – determined only at verification – is satisfied. This allows to keep the simple key generation of multi-signatures and support flexible threshold settings in the signing process later on. Both works use the same idea of combining BLS multi-signatures with inner-product proofs over committed keys. Das et al. give a somewhat generic proof from both building blocks, which we show to be flawed, whereas Garg et al. give a direct proof for the combined construction in the algebraic group model. In this work, we identify the common blueprint used in both works and abstract the proof-based approach through the building block of a commit-and-prove system for vectors (CP). We formally define a flexible set of security properties for the CP system and show how it can be securely combined with a multi-signature to yield a signature with ad hoc thresholds. Our scheme also lifts the threshold signatures into the multiverse setting recently introduced by Baird et al. (S&P’23), which allows signers to re-use their long-term keys across several groups. The challenge in the generic construction is to express – and realize – the combination of homomorphic proofs and commitments (needed to realize flexible thresholds over fixed group keys) and their simulation-extractability (needed in the threshold signature security proof). We finally show that a CP instantiation closely following the ideas of Das et al. can be proven secure, but requires a new flexible-base DL-assumption to do so.