What you're really referring to is a trusted device, of which you can have several:
Read the article:
Two-factor authentication for Apple ID - https://support.apple.com/HT204915
thoroughly. Various sections contain information that is key to you being able to set up and use a different telephone to get a verification code you can use.
"If your iPhone is your only trusted device and it is missing or damaged, you will be unable to receive verification codes required to access your account."
Read the sections about:
- Trusted phone numbers
- Manage your account > Keep your trusted numbers up to date and add a phone number.
- What if I can't access a trusted device or didn't receive a verification code?
And if necessary:
- If I can't sign in, how do I regain access to my account?
Sign into your account at https://appleid.apple.com/ and add your new number, then sign out of iCloud and back in again on your devices.
Get a verification code and sign in with two-factor authentication - https://support.apple.com/HT204974