Is there a way to compress multiple signatures of the same data? So, I'm working with a system that allows individual users to each have their own private-public key pair.

I would like to allow multiple users to use their private key to sign the same piece of information to confirm they agree with something.  By signature, I mean the public key can be used to check the signature is valid.

However, space is at a premium.  So is there a way to compress those multiple signatures of the same data?

Using Curve25519, but other algorithms might be acceptable.
You can use multi-signatures.

One example is the BN06 scheme described in the paper:
Bellare, Neven - Multi-signatures in the plain public-Key model and a general forking lemma