Like Doc Savage, Jim Anthony was a genius and a polymath with tremendous athletic abilities and a thirst for adventure. They would have had a lot in common. Both of them made their headquarters in New York City. They both had upstate New York estates and extensive holding around the country and the world. They both conducted extensive scientific research many times to aid the US government. And both were enemies of injustice who defended the weak against merciless criminals.
But they also both lived under great stress and needed to relax between missions. Jim and Doc used to go out on the town together in a way that Doc never felt free to do with his five aides. The two adventurers were very much alike but also different enough that they complimented each other. Jim was more of a playboy and was able to get Doc to "let his hair down " a bit more in public.
They were both musicians and would sometimes play with the Jazz bands in some of Jim Anthony's clubs. Doc was known to date several beautiful women during the 1940s and he often double dated with Jim and his fiances. Sometimes, the two adventurers would talk together long into the night and they were known to collaborate on special projects for days at a time with very little sleep. It became practical for Doc to have his own suite at the Waldorf-Anthony Hotel where he could retire after a long hard night. It was also a discreet place to entertain personal guests.
Jim Anthony probably filled a place in Doc's life that he been missing: a best friend. They probably had some interesting adventures together.