The best replacement for thrice is three times.

The best alternatives to thrice are rated as following:
★★★★★  three times
★★★  alkaline trio
★★  coheed and cambria
★★  trice
★  coheed cambria
  coheed
  twice
  thrice

Your alternative for thrice is not listed? Suggest!
Speaking about thrice, one probably shouldn't forget about animals as leaders.

Other search terms related to thrice and their ratings are:
★★★★★ animals as leaders
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thrice
three times
alkaline trio