How to open a second pop up, without closing the first one?

Hi Thiago,

Every site provides only one page at the moment (in terms of TestComplete and web browser). Popups, like provided on your screenshot, are usually implemented as child frames, divs, etc. of the main parent page.

I would advice to either investigate the staructure of the page in the Object Browser of Test Complete or record your actions (by recording the script code, but not keyword test) and examine recorded code.