that would contradict the lore and would be a retcon, since the only reason why super saiyan + God Ki'ed base-form is a thing is because
par example, king kai fist require the body work to multiply for it to multiply the energy usage, kaioken 10 would multiply the body work percentage from 100% to 1000%, that would be impossible and fatal for a human body unless if immortal though even then the body would just keep failing and regenerating in itself,
the reason super saiyan form cannot be used alongside king kai fist is because the body percentage is already over 50.000%, and to an impossible percentage of 400.000% for super saiyan 3, hybriding it with king kai fist would be a death wish,
as for the reason those points are mentioned, is because God ki doesn't add stress or overwork to the body, it simply pressure the energy to not leak, thus being hybridable with super saiyan, though multiplying that would break the God ki mode as the energy would leak thus revert back to ki.
it simply is not possible based in the current lore as it would require a retcon, which would be poor writing honestly, it better not to, there is already Super saiyan God ritual mode.
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