Can my car tow beyond its manufactured tow limit?

I drive a 2012 Dodge Durango SXT AWD 3.6L V6 with a max towing capacity of 6,200 pounds. It also has 167,000 miles on it.

Can I tow a travel trailer that exceeds my towing capacity? Such as a trailer that weighs right at 6,000 pounds or 6,700 gross weight.
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