Trivial real world case: Venus is about 98% of Earth's mass, and has roundly 100 times the Earth's atmosphere. This extreme atmosphere is mostly carbon dioxide, with the famous clouds composed mainly of sulfuric acid droplets.
The mechanismInterestingly, at altitudes just above the cloud tops, the environment is the most Earthlike to be found anywhere in the solar system off Earth -- pressure and temperature are very similar to Earth at sea level, though there's no free oxygen -- but it's probably the only place in the system where a human could survive with just a breathing mask and air bottle.
The mechanism that gave Venus casesuch a deep, massive atmosphere was probably (unless planetologists have changed their minds again) thermal outgassing of surface rocks as the runaway greenhouse took over a couple billion years ago.