I feel shia islam restricts polygami more than sunni-islam.
What are the conditions of getting a second wife? And is it recommended in shia islam to get a second wife?

If it's a big topic, I am okay with written articles/sources on it.

By default, there is no evidence that polygamy is mustahab. Yes, if there is a pressing need for it (such as to care for a widow or divorcee or even an unmarried woman, and there isn’t someone suitable to care for them, or let’s say one’s wife cannot conceive and so he marries another wife to have children), then it could become mustahab.

The conditions for it are:

1- One must be able to maintain justice among the wives

2- Marrying another wife does not lead to the destruction of the family and deviation of family members, as the Qur’an commands believers to protect themselves and their families.

3- If the wife stipulated in the marriage contract that he must seek her permission if he seeks to marry another wife, then he cannot do so unless she gives her consent.

4- According to Ayatollah Sistani, a man cannot marry a non-Muslim woman if he has a Muslim wife.