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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. Getty

She claimed in the docs when she and the NBA player first agreed on the $5.5K number , they lived together in North Carolina -- but things have drastically changed since she and the toddler moved to California late last year.

Renner said she "cannot afford the high cost of living given the current child support orders" ... and she added that with Washington exercising "less

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