Can a web server ask an SSOticket(TGT) client for a ticket for a "behind it" service?

Question

Active Directory

The network has a service with domain authorization. The service has some software API (not http) where you can log in by passing the client's SSOticket.
Is it possible to add a web server to the scheme between the client and the service.
Thus, the web server would request from the client (already a browser and not a desktop application) an SSOticket for the service described above.
Or the web service will not be able to do this, limited only by its SPN, which is set for a host in a domain of the form HTTP/[email protected]