Just combine all the entries into one (and note it in each post). It's the same idea as cross-sharing ANY kind of contest. You may be an influencer holding a contest and to get the most engagement you'd likely share it (the same thing) to as many places as you can. Of course, holding site-specific contests are good too.

It's all a bit nuts now, but I think (hope) it will chill out soon and we'll all get in the groove again.😊