"may mostly" is correct and usable in written English.
You can use it to indicate that you may have to do something primarily or mostly, as in "The project may mostly need a fresh set of eyes to get it finished."
Now in the short run, that may mostly be a problem for all of us.
The junta has said for years that it wants to shift to civilian government -- though these civilians may mostly be military men in suits.
The administration is already starting a review of the human space flight programs, so the appointees may mostly be implementers of decisions made at higher levels.
But the report's findings may mostly serve as a baseline from which to measure the impact that Facebook will have on location-based services.
After all, its mystery may mostly unfold on terra firma, but you can't imply railway intrigue without invoking the director of Strangers on a Train and The Lady Vanishes.
Higher rates of core inflation may mostly reflect the indirect effects of energy prices, but the Federal Reserve will need to be alert to the risks that high levels of resource utilization may put upward pressure on inflation.
Iron (Fe) deficiency in maize (Zea mays subsp. mays) mostly occurs during growth on calcareous or alkaline soils, where Fe becomes sparingly soluble due to its precipitation in form of hydroxides, oxides, or phosphates [ 1].
The genome of maize (Zea mays ssp. mays) consists mostly of transposable elements (TEs) and varies in size among lines.
(That may be mostly what the McVities want, too).
The European far right may remain mostly in the minority.
Microsoft's antitrust troubles may be mostly behind it.
