I was thinking on getting a sole 2fa wallet or standard wallet instead of getting a multi-sig again.
A standard wallet is a single-sig setup. A 2FA wallet is just a different type of multi-sig wallet, where you hold two of the signing keys and a third-party holds the third. I wouldn't use the 2FA wallet. If you want a standard wallet, go with the single-sig setup. If not, select a multi-sig variant you are most comfortable with.
But hypothetically would I be able to just have one wallet and make multiple copies of it and then put it on cold storage?
This is not a yes or no question. First of all, what are you planning to do with your copies? Also, there is no need to make copies of your wallet file if you make multiple physical copies of your seed and store them properly. The seed will recover everything, so don't bother with the wallet copies.
A wallet created on an online machine always remains a hot wallet. You can't create it on an internet-connected computer today and consider it a cold-storage from tomorrow. It has to be created the right way, and the keys have to stay offline at all times. A properly-airgapped computer with a Linux distro is the best option. The second best is an airgapped hardware wallet followed by a standard hardware wallet in third place. Everything below that (security-wise) is not a cold wallet.
Here is an example of a workable cold setup:
Electrum installed as a cold wallet on a computer with a cleanly installed OS (Linux preferably) with no network cards and ways to connect to the internet. You would then export the master public key and import it into an online desktop or mobile wallet. This online device serves for broadcasting transactions. The airgapped computer is the signing device that signs the transactions you broadcast with help of the online wallet.
This is not a cold setup:
Imagine the same setup as in the example above with the difference that you exported your seed/private keys and imported them into other wallets. Or, you created your wallet and seed on a hot wallet and now you want to "move" the keys offline.