ALISO VIEJO, Calif. — Quest Software Inc. said Monday that it received a higher buyout offer worth about $2.32 billion from an unnamed buyer, continuing a battle for the technology services provider.

The most recent offer, of $27.50 per share, follows a string of increasing bids that began after the company announced in March that it was being bought by the investment firm Insight Venture Partners for $23 per share. At that time, the company said the deal valued it at about $2 billion.

The March bid was a 19 percent premium to the company’s closing stock price the day before the deal was announced. The $27.50-per-share offer announced Monday would represent a 42 percent premium to Quest’s ending price of $19.40 from March 8.

Shares of Quest, which helps companies manage databases and provides other corporate IT services, rose $1.48, or 5.6 percent, to close at $27.70 Monday.

Quest said Monday that its board has decided that the most recent bid is superior to prior offers and that it has informed Insight and Vector Capital, which was added to the buyout group this month. Insight and Vector have three days to match the offer.

The $27.50 per share offer announced Monday would represent a 42 percent premium to Quest’s ending price on March 8.

While Quest did not say Monday who the other bidder was, reports published last month said that Dell Inc. was in discussions with Quest. Quest declined to comment further on who was behind the bid announced Monday. Dell also declined comment.

Earlier this month, an undisclosed party offered to buy the company for $25.50 per share, or about $2.15 billion.

Last week, Insight and Vector topped that with a bid of $25.75 per share.

If shareholders who supported the deal with Insight do not support the most recent offer, the company will grant the unnamed bidder the right to buy new shares of the company’s stock equal to a 19.9 percent stake, or pay it a break-up fee.