how can i make a part move locally that uses body position to move?

I'm trying to make a platformer in which I need moving parts that can move the player with them but I also need it to be done locally, to reduce lag. I have a local script that uses body position to move the part and also move the player with it but the body position doesn't work as it would in a normal script, I put the local script in starterplayerscripts. how would I go about making the local script function as a normal script would? also when I say the local script does not function properly I mean that the body position doesn't work unless the player is touching the part the body position is inside of.