Generally speaking, there is no such thing as simply "Adding" multiplayer to a game.
You'll basically need to recreate your game, taking into account host and peer setups and time difference between clients. The good part is that if you have your mechanics working properly already, you will have less problems to solve.
construct.net/en/blogs/construct-official-blog-1/making-snek-online-905 is a good read for the considerations that go into a multiplayer game, and then at least go through and do all the official multiplayer tutorials at construct.net/en/make-games/manuals/construct-3/plugin-reference/multiplayer
Then you'll have an idea what you'll need or won't need to make your game multiplayer. Not easy, but all the tools are there for you to do it!
A quick example of what changes when you go from single player to multiplayer:
Player presses button - > do action
For multiplayer it turns into
Player presses button - > Tell host you pressed button
Host receives player inputs - > Do action for that player, and tell everyone else what happened, taking into account the time it took for the message to travel
Everyone - > Receive what happened from the host, and update accordingly.
When you've got your multiplayer game set up, you can preview in multiple windows by holding alt when you preview, to test as if multiple peers are connecting to the game.