What are the limitations for amortizing the interactive session setup of MuSig?
Nonces must not be reused! In particular, in MuSig, nonces can not be reused
for other combinations of public keys or messages (also if everyone uses the
same public nonces all the time). This would leak private keys.

You pre-share fresh nonces by running multiple signing rounds in parallel.
With the library you link to
(secp256k1-zkp) this is
secure as you long as you keep the session states in memory and don't copy it.
Serializing the state and storing it on a persistent medium is not supported by
secp256k1-zkp and difficult to get right because if you accidentally use the
wrong nonce, you leak the private key.

A straightforward way to eliminate the overhead of the first two interaction
rounds is by attaching the nonce commitment and nonce to already existing
messages in your protocol. That way you would only have two parallel signing
sessions.

There is research being done on deterministic nonces for MuSig which have
zero-knowledge proofs that the nonce is derived correctly. With such proofs
nonces can be derived on demand from the signer set, your private key and the
message and there is no state to keep track of.