On Wednesday, Vista Equity Partners raised its bid for software maker SumTotal Systems Inc. to $4.85 per share which values the company at about $163 million.

San Francisco-based Vista said it would increase that offer to $4.95 if SumTotal's breakup fee with rival bidder Accel-KKR is invalidated or reduced.

Accel-KKR upped its offer from $3.80 to $4.80 on Tuesday and raised the breakup fee in a buyout agreement the companies had already signed to $6.7 million from $3.1 million.

The move on Wednesday was the third time when Vista has raised its offer after an original bid of $3.25 per share in April.

In a statement Vista's head manager Robert F. Smith said, "Vista is surprised and disappointed to learn that, in the midst of an active auction, SumTotal chose to sign an amended merger agreement containing an increased breakup fee without first giving Vista notice or any opportunity to raise its bid."

SumTotal, based in Mountain View, California, said late Wednesday that its board agreed on the fact that Vista's latest offer is superior to Accel-KKR's. But the company said that it is obligated to negotiate with Accel-KKR through May 26 to give that company the opportunity to enhance its offer and so it isn't making any recommendation at this time on the revised Vista Equity proposal.

Company Shares rose 7 cents to close at $4.88.