What can move, and what fights you
Water lines are the easy part of a renovation. They are small, they run uphill and downhill without complaint, and a competent plumber can get 1/2 inch PEX-A or Type L copper almost anywhere you want a fixture. Drains are the problem. A drain has to fall at 1/4 inch per foot on 3 inch and smaller pipe, and it has to reach a vent inside the distance the code allows for its size, which for a 1-1/2 inch lavatory trap arm is roughly a metre and a half of developed length.
Those two rules decide more bathroom layouts than any designer would like. Move a vanity six feet along a wall and the trap arm runs out of room before it finds the stack. Move a shower to the far side of a room with a finished ceiling below and there may not be enough joist depth left to hold the fall without notching something structural.
So the honest answer to whether a fixture can move is usually yes, at a cost, and the cost is measured in what has to open up. We would rather walk a layout with you before drawings are finalized than tell you halfway through demolition that the toilet has to stay where it is.