6.8 Remington (often called 6.8 SPC) was developed the result of a military search to replace the 5.56 NATO (as a veteran, I could go way off topic discussing that but will stick to answering your specific question).
It uses .277 caliber projectiles, same as the classic .270 Winchester, but uses a smaller case based on the old .30 Remington. So there's a lot of potential there for a versatile hunting and target shooting cartridge, particularly with all the reloading options out there and bullets developed for .270 shooters. It would of course, be a little more limited in bullet weights and lengths than .270, but should do everything a 6.5x55 can do, albeit without the decades-old reputation.