The CZ 550 Magnum has a longer magazine box than the CZ550 standard (30-06 length)
That means you need to get one of them too, or open yours up in length
Then the feed lips of the receiver itself need to be re-ground to feed the larger cartridge well.
When you are done with all that metal work you'll need to open up the front of your mag well in the stock to accommodate the extra length metal.
Or buy a new CZ 550 Mag stock. (Which I have to sell if you want one)

All in all it is not super fast and easy conversion, but it can be done. It may be a better deal however to simply buy a 550 in 375 H&H and keep you 270