Is it permissible to take back one's wife after a single divorce pronounced with the intention of divorce, and after the 'iddah period has ended without her being taken back, and then the husband deliberately utters more than three divorces after the 'iddah has ended?

A man's statement to his wife, "Return to your family after your 'iddah (waiting period) ends," is a kinayah (allusion) to divorce, and divorce occurs with it if the husband intends it. Since you intended divorce with this phrase, one divorce has occurred. If you leave your wife without revoking the divorce during her 'iddah, she becomes irrevocably separated from you, and no further divorce can occur after her 'iddah ends because she is no longer your wife.

If this was the first or second divorce, you may remarry her with a new marriage contract that fulfills its conditions (her consent, her guardian's approval, two witnesses, and a dowry). However, if it was the third divorce, she is irrevocably separated from you with a major separation (baynunah kubra), and she is not lawful for you until she marries another husband.

As for your remaining with her in the same house after the 'iddah ends, it is forbidden, and both of you must repent to Allah, as she has become a stranger to you.