How to inject my browsers to open a new tab when visiting a website

I use Windows with multiple browsers.
I would like to inject the browser with code capable of opening two websites at the same time.
For example, when I visit site.com or site.com/*, site.com opens, then another website opens in a new tab without closing the first site.
Or I would like to be able to have the code run on the site.com page or any other pages within the site if I click anywhere to open a new tab with specific sites.
It’s similar to the viral ads we encounter when visiting many websites, but I need to use it for personal purposes by injecting it into my web browsers, not the sites I visit, as I have no control over those sites.