Complex sentence: He Invited Payne to the club where he played with Morrison, hoping Morrison would invite him to join them, and after allowing Payne to sit-in on one performance, Morrison extended an invitation that Payne accepted.
Split into simpler sentences: He invited Payne to the club where he played with Morrison, hoping Morrison would invite him to join them. After allowing Payne to sit-in on one performance, Morrison extended an invitation which Payne accepted.