Dropbox was on pace for its best day since going public Thursday, with massive trading volumes sending shares up roughly 20 percent at their peak.

The stock hit an all-time high above $38 after closing Wednesday below $32. Shares were trading at more than 5 times their normal trading volume.

Thursday’s surge lifts Dropbox roughly 80 percent over its IPO price of $21.

Dropbox debuted on the public markets in March, soaring 35 percent on its first day. The company offers cloud storage for personal and enterprise use.

In an April note Piper Jaffray analysts led by Alex Zukin flagged Apple, Salesforce, Cisco, Google and Microsoft as companies with the potential to buy Dropbox.

Before Thursday, the stock’s largest single-day gain since its opening day topped out at 7 percent.

A company spokesperson did not immediately return a request for comment from CNBC.

—CNBC’s Jordan Novet contributed to this report.