I feel like the lowest-overhead way to manage such a theoretical would be to have a progressive tax rate that, in the higher brackets, negates the UBI.

That is, you give out $X to everybody, but everyone making over $Y+$X total has $X added to their taxes.

This feels a little silly on a but-you're-doing-things-twice level, but it lets a UBI program and taxes both operate independently without needing to cross-verify things, which allows for lower overall staffing and less in the way of possible bureaucratic loopholes for people to get stuck in.