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What about a Cooey tube magazine bolt action with a modified stock on it?
Other than that, I can't think of anything that would take .22 shorts in a rifle, there are some nice .22 short pistols out there but I haven't seen any rifles other than single shot or tube fed that take them
Winchester 69 & 69A's you can stack'im'oww you wish.
The photo above is a Winchester Model 131 and I've loded
up the mag with shorts, long and long rifles in no partickular
order and they feed/eject well.