If I were you I’d maybe check out a mastering forum or the mastering section at Gearslutz to find an answer from mastering engineers. They’d likely know more about translation between systems.
My 2 cents though is that your’re not really necessarily fixing “problems” with your mix. If you have perfect speakers in a perfect room and you love your mix then the mix is perfect. If that perfect mix is played back in an environment where it now doesn’t really work then that’s not the mix’ fault, it’s the environment. So really what you’re doing if you find that your mix isn’t working when checking on a “poor” playback system is you’re trying to change the mix so that it does, if you think it’s worth it.
It’s a compromise.
On the other hand you could be in a situation where your listening environment isn’t just ‘not perfect’, but it may have some serious defects. In that case a second set of speakers or a different environment may show you problems with your ‘main’ mixing environment. You could for example have an acoustic problem with the low end (quite common) in your main mix room, and even though everything sounds fine in the room once you put on some really good ‘reference’ headphones you’ll hear the problem. And you might also experience that same problem on a cheaper system. On the ‘reference’ headphones the bass might pop out at a couple of lower frequencies, something you didn’t hear in your room, and on a small set of speakers like a laptop you might not hear the bass that much but the speakers will distort because of that extra low-end energy.
So that’s sort of the other side of it…