A man may marry up to four wives, as explicitly stated in the Qur'an:
And if you fear that you will not deal justly with the orphan girls, then marry those that please you of [other] women, two or three or four. But if you fear that you will not be just, then [marry only] one or those your right hand possesses. That is more suitable that you may not incline [to injustice]. -- Qur'an 4:3
It's thus permissible under Sharia, and some Muslim men actually have four wives legitimately married before Allah.
It doesn't mean you're forced to do it. Indeed, alongside it's stated permissibility in the Qur'an, comes the warning "...if you fear that you will not be just, then [marry only] one...".
If a man is afraid that he will not be able to treat his wives justly if he marries more than one, then it is forbidden for him to marry more than one. -- Islam Q&A
It's also worth noting that having a monogamous marriage can be stipulated in the marriage contract, if desired.
If the wife stipulates that her husband should not take a second wife, this is a valid condition that must be fulfilled, and if he does take a second wife, she has the right to annul the marriage... -- Islam Q&A