sounds like a hell of alot of hassle mate... heres why...
1. Easy enough if you keep a common bolt face, but otherwise your up for a new bolt or bolthead aswell.
2. Your POI will shift everytime you switch barrels and have to rezero your scope each time.
3. Youll have to pay for not just the barrels, but also muzzle brakes
if you want them, a go guage for each barrel to headspace it when you switch barrels, muliple sets of dies and brass for each caliber etc... add all this up, its alot of money. Why not just go with the single largest caliber, in your case the 300RUM, and use it to shoot everything??? You can use all the money you saved on barrels, dies, brass etc to pay for bullets and powder? Youll be miles in front financially despite your using the most expensive caliber all the time.
I would spend good money and build super accurate custom rifle
in the largest caliber you might ever need, then you will never need another long range rifle for the rest of your life... i have reduced my gun collection to essentially 2 rifles that covers 99% of all the hunting i do. A big ass 375cheytac that covers all my long range hunting of ANYTHING out to some stupid distances, and a cheap 308win pump action with a 10shot mag (we not allowed semi autos here) with an Eotech sight for short range stalk hunting in thicker bush or forest type stuff... or i can pull the Eotech off the picatinny and drop a scope on it if the likely shooting distances are gonna be a bit longer, like 100-300yds etc... 2 rifles covers every type of local hunting situation i could be in and im willing to bet cost less than trying to run a 3 swtich barrel setup.
I could understand running a 2 barrel setup, like a 300RUM for hunting big stuff way out there, and maybe a 6.5mm or similar switch barrel for target/cyote use because a target rifle and LR rifle are physically very similar, both need high accuracy components and you can save a bit of money by sharing the scope, action and stock etc. But 3 just doesnt make sense...