It seems that different online dictionaries gave me different answers:
Is 企 a heteronym?
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Yes and no.
If you check out Liang'an you'll see it mentions:
So basically what that tells us is: Mainland (i.e.: PRC) is qǐ, while Taiwan is qì.
It's a regional -or- topolectical thing, rather than a character with different pronunciations at different times.