My experience is that it's usually the low strings that run out of room because they're the ones being pulled back, but if the bridge is in the right place, and the nut cut properly, there should be enough room to intonate most strings if you use regular or a gauge heavier/lighter.
What kind of guitar is it, or I guess, what kind of bridge, and what gauge strings are you putting on?
Also, if a string does not seem to be changing regardless of what you are doing, it suggests either the string is "false" and needs replaced, or there's something else in the setup going on that's causing it. Having a pickup too close to the strings can create problems, as well as frets that are slightly high.
And, assuming you're using any of the modern clip-on or inline digital tuners, can you post a video of you setting the intonation of those 2 strings, e.g., showing the string tuned to pitch open, and then fretted at the 12th fret (for starters)?