BayPine, a private equity firm founded by veterans of Silver Lake and Blackstone Inc., raised $2.2 billion from institutional investors for its first fund.

The firm has about $3 billion of capital, including co-investments, that it will use to acquire stakes in established middle-market firms and help them overhaul their digital strategies, Boston-based BayPine said Thursday in an emailed statement.

The firm has already completed three acquisitions, including Mavis Tire Express Services and Pinnacle Dermatology Management. BayPine helps its portfolio companies use technology to improve their sales and customer experience, allocate resources, and make other operational improvements.

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