I was thinking about this question recently due to the British gun laws.
Here in the UK, all semi-auto rifles, which are called “self-loading” in British terms are classed as Section 5 (Prohibited) firearms. There is an exemption in the law that states “unless chambered for .22 Rimfire cartridges”. The description goes into no more detail than that. As such .22 Short, Long/LR and .22 Magnum are currently legal.
There are no further limits placed on the type of firearm, magazine type/capacity or fixed/detachable mag. The only other conditions are that it that it must be a minimum overall length of 24", with a minimum barrel length of 12".
This made me wonder if a bottle necked .22 Rimfire cartridge with a higher powder capacity was possible. I know that rimfire pressures are limited by the construction of the case.
That again made me wonder about the possibility of steel or stainless steel cases rather than brass.
An AR-15 type rifle chambered in this new calibre with 30 round magazines is the type of firearm I am thinking of. Unfortunately I doubt that anyone here would risk developing it, as the government would likely change the laws. It is still interesting to consider if it is theoretically possible.