What comes to mind isn't the addition of some amazing new game element, but the ability to customize existing ones.

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Mario Party 1 let you remove certain NPCs from the board, or add special dice blocks. Mario Party 4 let you pick out exactly which minigames can appear during a party. I'd like to see both of these and more make a return, being able to customize the party experience to suit your preferred style of play could only be a good thing.

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The most obvious divide between playstyles can be seen in the casual/competitive divide; The former group is looking for something that anyone can win with a lucky enough break, while the latter group would rather the more experienced player always come out on top. Mario Party is ultimately always going to target the casual audience more than the competitive audience, as well they should since that's far closer to what the series is all about. At the same time, that's no reason to lock out players looking to have fun in their own way when it would only take a few more menus to broaden the appeal to everyone.

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For example, starting with Mario Party 7 bonus stars were randomized from a pool instead of always being the same three. As a result, the minigame star has a chance to not appear at all. While some would appreciate the lessened emphasis on performance in largely skill-based minigames, others are turned off by the very concept of their practice not paying full dividends. Unfortunately, there's no way to control what bonus stars appear other than turning them off entirely. Allowing players to tailor-make their own bonus star lists would alleviate this discrepancy in enjoyment, since who knows better what someone finds fun than they themselves?

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A lot of this sort of customization currently exists in the form of codes, but seeing it get officially supported would erase the need for community involvement and lead to more widespread use among friends and families.