I think with the CTE epidemic which will really accelerate in the next decade or so that if Brady wins a fifth Super Bowl or more then I think it is unlikely a player will ever break his record for one team.
One possibility would be if there was an unlimited cap and owners could spend what they wanted to enable them to win. This is unlikely to ever happen but if it went the way of NBA in the past or MLB then I could see someone like Jerry Jones or a potential future owner buying up much of the premier talent and one side dominating for a decade. This would also mean other teams would get worse and the competition would not be as interesting between sides which would likely lead to even more fans turning the game off on tv.
One possibility would be if there was an unlimited cap and owners could spend what they wanted to enable them to win. This is unlikely to ever happen but if it went the way of NBA in the past or MLB then I could see someone like Jerry Jones or a potential future owner buying up much of the premier talent and one side dominating for a decade. This would also mean other teams would get worse and the competition would not be as interesting between sides which would likely lead to even more fans turning the game off on tv.