There is no reason why you cannot do this. JWT is really nothing special, it's just a token, similar to a session id token. The difference between a JWT and any other token is that it can contain a data payload.
What you are describing is essentially providing an OAuth 2.0 password. Your single sign-on system is an authorization server that can authenticate users and provide them with an access token. In this case, the access token may be JWT. Then users (resources) can use their access tokens to access resource servers (other other related domains), these resource servers can verify that the access token is valid and allow or deny requests.
I use the following library when implementing OAuth 2.0 in PHP: https://oauth2.thephpleague.com/ - there is also good information in the docs there.
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