Is it possible to link multiple bitcoin addresses under one private key?

It is possible to derive different addresses from a single private key, namely one address from the private key's compressed public key, and one from the private key's uncompressed public key.

If you sent bitcoins to each of these two addresses, they would exist as separate UTXOs, even though the same private key could sign to spend the funds in either address.

This would make signing raw transactions easier.

I'm not sure what is meant by 'easier' here, but in general, it is advised that users do not handle keys themselves, rather let the software take care of this.

Perhaps also worth mentioning: BIP 32 HD wallets allow many keypairs/addresses to be generated from a single seed/extended key. However each address generated in the HD wallet can only be spent by signing with the private key associated with that address. A parent extended private key cannot sign for child address transactions (it is instead used to derive the child private keys, which can then be used to sign transactions).