No. In a helping profession, you need clear boundaries. There are many risks, including favouritism. If you do something for one client, it’s hypocritical and unprofessional to not treat the other the same. As well, considering the clients state, blurring/crossing boundaries can cause more harm than good. Regardless of what helping profession (nurse, doctor, therapist), you need boundaries. What would happen if you stayed 20 min extra to talk to one patient per shift. Well, another patient sees that and wants the same extra care - outcome = bad review, distrust, as well, the helping professional is now overworking them self.
These are just small snippets of examples of why it’s not a good idea to mix this kind of work with friendship/pleasure. If you two are dying to be friends, then get a new therapist. I know from experience (not with a therapist), that although you may believe you can maintain boundaries, the other person may drop the ball and trip you up..HARD.