Yes, there is a phenomenon of "caliber creep," but there are some parameters that can help.
For one, a person should take a significant step "forward," not an itsy-bitsy micro-step. If you want to try a more powerful cartridge, then choose something that is significantly more powerful. For example, a person with an excellent 243 should probably not be considering a 257Roberts or 25-06. The 257 Bob and 25-06 are EXCELLENT cartridges, but they are not really a significant upgrade in power. The bullets are only marginally heavier and only 1 caliber wider.
(Disclaimer: I started out hunting with a 270. So for caliber creep I ended up with a 338WM for my particular circumstances in Africa, then 416 and even a 500 wildcat. My wife shoots California deer with 110gn TTSX, 118gnHH in 270. When we wanted something even lighter for grandkids in the US we went with . . . the 243.)
A significant "step up" might land in the 'three-sisters' category: the 270Win, 280, and 30-06. All can handle good elk bullets, especially 28 and 30 caliber, though the 270 has a slight advantage for flat-shooting deer bullets that exit. That threesome can be upgraded in powder capacity, like the 7mRM, 300WM and 300PRC. However, a person must remember that they are shooting the same bullets. One may notice the 308 missing in this list, and I just got a 308 for grandkids a couple of years ago. That was because I wanted a lightweight rifle (think Kimber) that would be good on hartebeest, and the 308 would definitely be better than a 243 in the African bush. And I didn't want a heavier rifle or a magnum for the kids.
Meanwhile, before creeping up in caliber, consider the option of upgrading bullets. We've recently been loading the 70gnHammerHunter in the 243. The little 20" barrel still does 3550fps. If your 243 has a 24in barrel you can expect 3650-3700fps. That is screaming. The petals will take out the lungs and the cylinder bullet will exit the largest mule deer that you can find. These new bullet technologies do the "power creep" for us without needing a new caliber. So maybe start there, and then for an upgrade get something significant in terms of diameter and power, at least a 270Win, or more powerful.