Mechanically linking multiple motors for a gearbox

Is it feasible to mechanically link 3 motors together; and what exactly the setup might look like. Can I used 1 encoder if the 3 motors are mechanically linked together. Is there a way to split the output signal of the one motor driver to the three motors safely?

If we must use different motor drivers for each motor, how could I make sure to be able to call calibration on the three drivers at the same time so they calibrate in sync? I feel like three encoders that are mechanically linked to spin at the same angle is kinda not necessary so it would help reduce redundancy and obviously total cost.

Context: trying to make a multi motor gearbox.

It is feasible to link them mechanically, but in most cases it’s easier to design around a single (usually larger) motor, what is the application?
Since the encoder is also providing position for the controllers commutation it is best to have the encoder connected directly to the motor shaft, but a very tight (minimal play/backlash) gear train can also work. I’m not sure how you would address diverting the encoder signal to all three controllers, this would probably depend on the encoder type.
If by ...split the output signal of the one motor driver... you mean the three power phases then no, you should not do this. This comes back to the issue of commutation feedback, the three motors are not necessarily locked into the same electrical phase so each motor will need its own controller to handle phase switching.
I can think of two ways to get around synchronized calibration: Use an absolute encoder that does not require calibration after a reboot, or only calibrate one motor at a time (making sure the other two are both idled)

okay, that makes sense in terms of splitting the outputs so thankfully lol, the explanation makes sense.
I’m curious because a long time ago in FRC (HS robotics) I think I remember using PWM splitters to clone the signal of the motor driver(s) therefore effectively getting them to all respond to the same input signal from the controller to drive the motors in a gearbox essentially “together”. It was the drivetrain so maybe it was for a non-precision setup and It was a DC brushed motor called the CIM motor. I was wondering if like I could mechanically link the three motors onto a single encoder and then split the signal from the encoder to the three drivers.
The hardware
The encoder AMT212B-V-OD which is an absolute encoder
Odrive S1(s) but I also have the pros which I only swapped out bec of the whole brake resistor allows for more rapid direction changes and speed changes.
Motors: D6374 150KV

Sorry if this is really trivial, Im just wondering if I could get help before attempting ideas that might be well-known. Appreciate the help always.