Provided you have full permission to use all of the assets in your game (art, music, etc.), it's your property so you can do with it what you want. When you submit your game to a distribution service, be sure to carefully read the terms and conditions - you might be giving up your right to freely distribute the game to other services.
The only disadvantage to distributing to multiple services is that it requires more effort to keep all of them updated as you make changes to your game. Otherwise, it just means more people will play it, which can only be good.