Separate to the conversation of how to do what you want, is a conversation about the best way to do something similar. Pick a parent case, then neck it up and down for all the bullets you'd like to use, that gets you inside the performance envelope you want. Pick the action and magazine length that fits best. Tune a couple magazines for each cartridge individually, as each bullet is likely gonna want to be presented to the chamber a little differently. Then it really is change barrel, load magazines, shoot.
For example, you'd be hard pressed to find a better all around performing case than the 30-06 family. From 6mm-06, to 6.5-06, .270 Win, .280 AI, .338-06, and .35 Whelan, not to mention the granddaddy. If you want higher performance, go with the RUM family, so long as you don't mind the recoil, and the smaller overbore versions taking your lunch money in barrel life.
If it was me, I'd do 3 barrels, 6.5-06 at 26", throated for 142-147 grain class bullets, which will beat the pants off a 6.5PRC for straight performance 7 days a week, and twice on Sundays, a 30-06 with a Serengeti chamber, at 26-28", which knocks on the door of 300WM easily, and gives me access to a wide range of good bullet weights for lots of things, and a .35 Whelan at 20-22", for a shorter handier rifle when I want a gun to go hunt with.
Run the numbers for the cartridges you want, and think hard about what your overlap is. 6.5 Creed gives you most of the performance of 6.5 and 7 PRC, at least for paper targets, and it isn't til you get to the 300 that you're really into a different animal. Now, if you're talking 7-300 PRC, then you're into a totally different performance class than the aforementioned cartridges, and the only thing I mentioned that would be comparable would be the 7mm RUM.
This is all worth what you paid for it, but take it from a guy who's been down the road you're on and decided the juice isn't worth the squeeze in almost all cases.
