Of the top of my head.
Possible excessive play in steering/suspension linkages.
All vehicles can "torque steer" to varying degrees between next to zero
and excessive (but never dangerous as they would never be homolagated).
If there are no bad linkages then torque steer is a function of
differential and drive shaft design. Basically equal drive, symmetrical
drive to the wheels, be they front or back. Anything that upsets this
symmetry will induce unequal drive.
Loose steering linkages/suspension bushes will allow the wheel to turn
in or out as it is driven. This turn will effectively turn the vehicle.
On a front wheel drive vehicle then the wheel opposite the turn
direction is the major driver. i.e. when you turn to the right it is
the left wheel that is the major director.
So, for you problem I would initially focus on front left wheel turn in
when being driven hard.
This is just a start. It could be the right wheel assembly bit left is
where I would start.
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