R. Kelly -- What's Another MILLION in Unpaid Taxes?

R. Kelly has a "put it on my tab" approach to his taxes ... because TMZ has learned his ever-expanding tax bill has just increased by more than a million bucks.

According to documents filed in Illinois, the "Trapped in the Closet" singer owes Uncle Sam a cool $1,379,695.11 for unpaid taxes for the year 2011.

As TMZ first reported, Kelly already owes $4,848,072.71 in unpaid taxes for the years 2005-2010. That brings his total to a cool $6,227,767.82.

Seems his accountant has been trapped in a closet for the past seven years.

A rep for Kelly tells TMZ, "He takes this very seriously and is already communicating with the IRS about the payment process to quickly resolve the issue."