Is it possible to take back a wife after divorcing her three times (once initially, then twice more) over separate periods, given the strong desire to take her back?

If you have divorced your wife with a triple talaq, it is not permissible for you to remarry her unless she marries another man out of genuine desire and he consummates the marriage, and then he divorces her and her waiting period (iddah) concludes. However, if the divorce is not an irrevocable major divorce (baynunah kubra), you can reconcile with her during the waiting period (iddah). If the waiting period ends, it becomes a minor irrevocable divorce (baynunah sughra), and you can marry her again with a new contract and dowry if she agrees. It is advisable to consult Sharia courts to rule on such matters.