General synonyms:
* Agree
* Acknowledge
* Receive
* Take
* Embrace
* Endorse
* Approve
* Admit
* Tolerate
* Permit
* Allow
More specific synonyms:
* Concede (to acknowledge reluctantly)
* Submit (to yield to authority)
* Acquiesce (to accept something reluctantly)
* Embrace (to accept something enthusiastically)
* Welcome (to receive something with pleasure)
* Adopt (to take something as one's own)
* Undertake (to agree to take on a task)
* Underwrite (to agree to support something financially)
* Subscribe to (to agree with a belief or opinion)
Other options:
* Take into consideration
* Take on board
* Come to terms with
* Be reconciled to
* Make peace with
The best synonym will depend on the specific situation. Consider the context, the speaker's intent, and the desired tone.