Can a husband who has divorced his wife by uttering the divorce pronouncement three separate times, and entered into two new marriage contracts, and had a divorce ruling issued by mutual consent, take her back?

The minimum number of divorces that can be counted against you is three: twice by your utterance, and the third by a judge's ruling. Therefore, your wife has become irrevocably separated from you with a major separation (baynunah kubra), and you cannot take her back until she marries another man, and he divorces her, and her waiting period (iddah) from him ends. It is essential that this marriage be out of genuine desire and not a temporary marriage intended solely to make her lawful for you again (tahlil).