Quest Software (QSFT) threw its weight behind a sweetened buyout bid from Insight Venture Partners late Tuesday as the bidding war over the software company continues to evolve.

The agreement, Quest’s second this year with the venture capital investment firm, is worth $25.75 a share, representing a 12% increase from the original $23-a-share bid.

It also trumps a less lucrative takeover offer valued at $25.50 a share from a mystery bidder that Reuters identified last week as PC maker Dell (DELL). The apparent Dell bid arrived during a “Go Shop” period that allowed Quest to solicit other offers.

Based in Aliso Viejo, Calif., Quest sells software that is used in enterprise systems management. The company, which was founded in 1987, employs nearly 4,000 people and generated almost $900 million in sales in 2011.  

The sweetened Insight deal now includes private-equity firm Vector Capital to the buyout group.  Vector is based in San Francisco and manages about $2 billion.

The companies said the deal will be financed through a pair of equity investments worth $187 million each from Insight and Vector, a rollover of at least 84% of CEO Vinny Smith’s existing shares and about $1.2 billion in debt financing from J.P. Morgan Chase (JPM), RBC Capital (RY) and Barclays Capital (BCS).

Shares of Quest continue to trade above the offer prices, indicating the markets believe an even more lucrative bid could emerge. Quest was recently off 0.6% to $26.38.

Morgan Stanley (MS) is serving as Quest’s financial advisor.

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