Heading into New Adventures territory here.
As I understand it from explanations of the incomplete Cartmel Master Plan, the Other is the mysterious trickster of the Rassilon/Omega era, and was a pre-Hartnell, pre-regeneration-cycle Doctor. Or maybe all the pre-Hartnell Doctors. Or...
He partially manifests in the Seventh Doctor, which is why he’s “far more than just another Time Lord.”
Or something like that.
So what if this is something Time Lords could do, back in the day? Like storing their power in a Chameleon Arch, or taking the potions of Karn.
They could program themselves - or their descendants - to regenerate into specific forms under specific circumstances.
And since not every Time Lord has much control over their regenerations (the Doctor far less than most, it seems) they might not even know about it until it’s too late.