Brittany Renner wants a court to increase P.J. Washington's child support payments to her -- saying in a new filing this week $5,500 a month is just not enough.
Renner made her case to the judge in documents that TMZ Sports has obtained ... asking for "at least $35,000" a month from Washington in an effort to raise their 4-year-old son in a manner suitable to a kid with such a rich father.
She claimed in the docs when she and the NBA player first agreed on the $5.