FROST requires each signing party to share a nonce, and the signing parties sign under the same agreed upon set of nonces.

You can share a whole bunch of these nonces upfront, storing them on the coordinator wallet ready for use. This way, signing can still be done in a single round.

A difference with FROST however is that you need to select the subset of signers (signer_2, signer_3, signer_5) that will be signing, from the beginning of the signing session. If this was a big deal then you could use tricks like combinations of concurrent signing sessions.