Well just redesign it to withstand the stress of the rifle round.
In other words, start again almost from scratch and end up with a weapon based on an operating system that nobody wants to use any more.
Regarding weapon actions, Maybe manufacture somthing well tried & reliable like the Bren/M1918 BAR/FM-24 Chatellerault/FG42 but scaled down as a 5.56 assault rifle.
Don't be absurd. Apart from the FG42 (used in only one limited production and obsolete weapon) these are all very old MACHINE GUN actions; why would you want to use them for a rifle? They all fire from an open bolt. In case you weren't aware, rifles are supposed to be ACCURATE.
Some well-tried and reliable rifle actions:
FN-FAL, AR-18, G36, AK, FNC, M14.
Put these together with promising new designs like the HK416/417 and FN SCAR, and there is clearly no shortage of decent rifle designs. Why create a pointless fuckup like a 5.65mm Calico - which would just be an inferior rip-off of the HK33 - or something designed around a completely unsuitable MG action?