I have never used this but this add on found by searching signature switch on the add on page claims to do what you want.

https://addons.mozilla.org/en-US/thunderbird/addon/signature-switch/?src=search

Signature Switch works well on my system. It can be manually set to use one of a set of signatures, or can be automated to display a specific signature based on the recipients address or even a mailing list name. It recognizes different identities and changes the signature accordingly.

Signature Switch 1.6.13 by Achim Seufert https://addons.mozilla.org/en-US/thunderbird/addon/signature-switch/

TB-38.3 Win10-PC