A for-profit business could accept donations. But the people making the donations will not have the tax benefit of deducting those donations from their taxes. Mixing for-profit and non-profit operations together is like mixing oil and water.
Depending on what your goal is, you may need to set up a non-profit entity.
This answer is provided for informational purposes only. Legal advice can only be given in an office appointment by an attorney licensed in your jurisdiction with experience in the area in which your concern lies.