Yes, in general, a PR can work two jobs in Singapore as you will have largely similar rights as a full Singaporean citizen. Let us explain more below.
What is moonlighting and is moonlighting legal?
Moonlighting basically means you already have a full time current job, and are seeking part time concurrent employment or a second job at a different employer.
Whether having two jobs with different employers is allowed or is legal for you as a permanent resident under Singapore law depends on your current business employment contract at your one job.
Are you employed in the public service division?
If you are a public or civil servant in Singapore, meaning you work at a Singapore government related organization, they will almost always prohibit you from moonlighting, or having two jobs. This is case for both citizens and PRs.
What if you need the extra pay to supplement your salary?
If you are a civil servant employee but want a part time job or second job on top of your full time job for extra income, you can try to seek approval from Ministry of Manpower depending on your circumstances. Sometimes an additional part time job may be approved on a case by case basis.
Are you working in a private business right now?
If you are working full time in a private company, which many are, then it depends on your employment contract terms with the current employer you are with. There is no hard and fast rule when it comes to this, and it is almost entirely a private matter between you and the company.
Work permit or work pass holders or S pass holder usually cannot, but a permanent resident is usually allowed as long as there is no conflict of interest between the two businesses or career options. Conflicts may occur if you try moonlighting in the same industry.
Difference between a PR and pass holder
The biggest difference between those people are permanent residents and those who are holding any kind of employment pass is that the former can still stay in the country indefinitely regardless whether they still hold their job, can switch jobs readily and can also work at more than one job subject to the above disclaimer. However, the latter is almost exclusively barred from taking on any work other than the one that their pass allows them to.
Singapore is very popular among young couples, and while there is no doubt that Singapore is one of the best places to start a family, it is far from the cheapest.
Therefore, many employees have concerns when it comes to money, and wanting to know if a permanent resident can work 2 jobs is a highly justified question. Rest assured, unless your contract specifically prevents you from doing so, or for example you are an employee at a government related organization, you definitely can work 2 jobs.