As of May 2020, WWE has instituted the "Brand-to-Brand invitation" rule, which allows wrestlers to appear on another brand "four times a year," implying it will go on longer than a year. However, details are few and far between as to what constitutes a Brand to Brand invitation.
On September 11's Smackdown, the rule was referenced as "once a quarter, a Raw or Smackdown wrestler or team can appear on the other brand." It can be assumed -- as if such a thing can really happen on WWE programming -- that only wrestling a match actually counts, and the act can appear on both shows during the build up.
Fightful will keep a running list of instances, and this article will likely evolve as more happen. You can see the active WWE roster at this link.
Baron Corbin (1): WWE Raw match with Drew McIntyre on May 18.
Shinsuke Nakamura & Cesaro (1): Appeared on WWE Raw September 7, wrestled on September 14.
Street Profits (1): Appeared on Smackdown September 11.
AJ Styles & Omos (1): Appeared on WWE Smackdown on January 29, 2021 to face Daniel Bryan.
Baron Corbin (1): Appeared on WWE Raw August 9 to face Drew McIntyre.
At some point after the WWE Draft, this appears to have been abandoned. Kevin Owens and Lucha House Party both appeared on NXT programming, but the rule was never mentioned on WWE TV again after this.
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