Brazilian Jiu-Jitsu has been proven to be an effective self dense system, however many of its detractors bring up the case of multiple attackers.
In reality, there is no perfect martial art against multiple attackers.
As Navy Seal and BJJ black belt Jocko Willink says, the best strategy is to run:
Here are some video highlights from a self-defense/combatives seminar that was taught by BJJ and Judo black belt Brian Jones of Valhalla Academy. Jones is a black belt under Carlson Gracie Jr.
There was more to the seminar but this part focused on preventing takedowns, getting up, and getting away.
In this video, Rener Gracie adresses the question and offers a simple solution: Run.
If you cannot run, and are trapped, here are the three universal principles of self-defense as taught by the Gracie Academy, so you have a better chance of survival if you ever find yourself in a multiple attacker situation.
Principle 1: Diffuse the “Combative Energy” of the interaction.
Principle 2: Evade their attack with effective distance management.
Principle 3: Attack first and attack fast.