Is there a limit as to how many antihistamines a person can have in a day?

Antihistamine limits: While most antihistamines are very safe you should never use more than the recommended dose without the guidance of a physician. The consequence of too much antihistamine could include increased side effect like sedation or even toxic overdoses which can be severe.

Yes: Doses of medicines are chosen by how well they do in clinical trials before reaching the pharmacy. For example, if the dose is 10 mg higher doses provide provided no additional benefit or increased toxicity. I would advise you use the prescribed dose unless otherwise suggested by your doctor.