Alice, Bob, and Carol each generate ECDH keypairs. Alice and Bob establish a communication channel and negotiate an AliceBob secret.
The question is: Is it safe for Alice and/or Bob to reuse their keypairs to negotiate a new AliceCarol and/or BobCarol secret?
The intended use is authentication. Each party can persistently store the others' public keys, and persistently store or deterministically recreate their own private keypair. Each party could establish a new communication channel with another party at a later time, verify that the other party's current public key matches their previous public key, generate a random message M and send it to the other party. The other party can then use the negotiated secret to HMAC sign M to generate M' and send M' back. At this point, M' can be verified by the originating party re-calculating M' using the negotiated secret, thus validating the other party's identity.