The best replacement for may is might.

The best alternatives to may are rated as following:
★★★★★  might
★★★★  can
★★  dawn
★★  shall
★★  could
★  misty
★  might grammar
★  ash
★  drew
★  will
★  can grammar
  stritch
  ann
  mae
  dawn episode
  might usage
  might as well
  must
  should
  jimmy page
  lou holtz
  james may
  mayroon
  maybe
  dawn pokemon
  tiger woods
  chef mickey

Your alternative for may is not listed? Suggest!
Speaking about may, one probably shouldn't forget about ash.

Other search terms related to may and their ratings are:
★★★★★ ash
★★ jeff beck
★ flyleaf
sarah frater
You have in mind a companion for may and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of may in all years. Click on graph for more.
may
might
can