Supply is never what decides a layout. Small-diameter flexible runs go almost anywhere a wall or floor cavity exists, so a tap can be relocated without much thought. Waste is the opposite: it moves by gravity alone, needs continuous fall, needs a vent within reach of every trap, and travels in a pipe large enough that the floor structure has an opinion about where it goes.
That produces a clear order of difficulty. A basin is the easiest fixture to move: small waste, generous permissible fall, a pipe that fits inside a stud wall. A shower is harder, because its trap sits below the tray. A toilet is hardest by a wide margin. Its drain is the largest pipe in the room, it runs at a conventional fall of around 2 per cent — a quarter inch per foot — and it has to reach a stack. Every 300mm of horizontal travel spends 6mm of drop, so a toilet moved three metres has used 60mm before it arrives.
Joist direction turns that arithmetic into a cost. Running parallel, between joists, the pipe has the depth of the bay to work with. Running perpendicular it cannot simply pass through: a hole large enough for a toilet drain exceeds what may be bored through a joist of ordinary depth, and the pipe is falling as it crosses. The options become dropping below the joists and losing height in the room beneath, reframing with headers, or building the bathroom floor up and accepting a step at the door.
Venting is the part people forget. Every trap needs one, and the arm between them is limited in length and fall — exceed it and the trap siphons dry, which is how a relocated fixture starts smelling months later. A basin moved along a wall away from its vent is not an extension; it is a new vent. Grouping fixtures near the stack, where a bathroom group can often be wet vented, stays cheaper than spreading them out.