There are several synonyms for the phrase "turn over in one's mind", which means to think about something deeply. One can contemplate, ponder, meditate on, and reflect upon an idea or concept. Additionally, one can mull over, chew on, or ruminate on a thought or issue. One can also consider, weigh, scrutinize, and evaluate a decision or course of action before making a choice. All of these synonyms emphasize the active engagement of the mind in assessing and analyzing information in order to arrive at a deeper understanding and make informed decisions.