The lukewarm response could be due to PMEs not knowing about the centre, as well as their own workplace rights in general, National Trades Union Congress (NTUC) assistant secretary-general Patrick Tay said yesterday.
"Many may not be aware of the first centre as it is co-housed within e2i," he said, referring to NTUC's Employment and Employability Institute in Jurong East.
They may also not know about recent legislation changes, for example, to the Employment Act, which was amended earlier this year, added Mr Tay.
But NTUC remains undeterred. Yesterday, it opened a second such centre in the Central Business District.
This will help it to " better cater to PMEs", it said in a statement.
The centre consists of two counters where PMEs can get career and legal advice, and is housed within NTUC's Members Hub at the basement of One Marina Boulevard.
NTUC also launched an online portal where PMEs can log on for similar information.
It will couple these efforts with campaigns to raise awareness of the centres, said Mr Tay.
Union members will get to enjoy a "full suite of services". These include membership privileges such as dining and travel discounts, as well as certain legal services.
Non-members will have limited access.
"We will still give non-members a basic level of advice on where to go, what to do. But for a more in-depth understanding, be it going through their contract or representation at the union level, that is for members only," said Mr Tay.
Non-member Damien Yee, 37, an IT head of training, said he would make use of the centre or even sign up as a member.
"I'm interested in advice on career progression, and leadership forums where I can meet with other CEOs," he said.
Mr Allen Lim, 49, who is a director of learning and development, and works with PMEs in the Asia-Pacific, said the centre would be useful for those in their 40s looking to "consolidate their expertise and find new things to do".
"In Singapore, we find that people at that age get stuck... They just stay at that job and retire. But in other countries, people in their 50s are still looking for new things to do," he added.