Plato Learning Inc., an online education company based in Bloomington, raised its bid to acquire Wisconsin Rapids-based Renaissance Learning Inc. on Monday for a second time.

Plato proposed to acquire all the shares of Renaissance Learning for approximately $496 million or approximately $16.90 per share. Plato raised its bid from about $471 million, or $16.01 per share, that it had made on Sept. 27. Plato initially bid $15.50 per share in late August.

Renaissance Learning provides technology-based school improvement and student assessment programs for K-12 schools. On Aug. 15, Renaissance announced that it had a definitive merger agreement with Raphael Holding Co., a company formed by European private equity firm Permira Funds, for approximately $440 million. Permira's latest bid was for $455 million.

A special meeting of Renaissance shareholders has been scheduled for next Monday. Renaissance co-founders Terrance and Judith Paul and related family interests control 69 percent of the company, and they had pledged their shares to the Permira offer.

Besides the total values of the competing offers, the bids differ on how much would go the "Paul Shareholders." Plato's latest offer allows the Renaissance board of directors and the Paul shareholders to allocate the merger consideration in any manner.

Private equity firms have been acquiring private education firms lately. Last week Providence Equity Partners completed a $1.6 billion acquisition of Blackboard Inc., a Washington, D.C., based provider of enterprise technology for online learners. Plato Learning was itself acquired by private equity firms Thoma Bravo Partners and HarbourVest Partners in May 2010 for approximately $143 million.

Shares of Renaissance Learning (RLRN) closed Monday at $17.01, up 2.0 percent.

Patrick Kennedy • 612-673-7926