BasePart:MoveTo(CFrame, time)

This seems quite similar to another feature request in that both wants some interpolation of given properties.

I’ve put up a fairly simple solution, but it’d be better to have a TweenService handle that sort of stuff for us - I do agree with sparker22 and GollyGreg’s points on this issue. All the solution in the link above would solve is the actual interpolation - so you’d either tween on the server, or signal all clients to tween using a RemoteEvent. Problem is just that there’s no guarantee when the signal reaches the client, so everyone will see the part you’re tweening/interpolating at different times.