It’s stronger than that: you must have it transferred. The law is pretty clear:
Full text of the law:
[DE] Bundesgesetz über die Freizügigkeit in der beruflichen Alters-, Hinterlassenen- und Invalidenvorsorge (Freizügigkeitsgesetz, FZG): Fedlex
[FR] Loi fédérale sur le libre passage dans la prévoyance professionnelle vieillesse, survivants et invalidité (Loi sur le libre passage, LFLP): Fedlex
[IT] Legge federale sul libero passaggio nella previdenza professionale per la vecchiaia, i superstiti e l’invalidità (Legge sul libero passaggio, LFLP): Fedlex
Relevant articles (3 and 4) loosely translated by yours truly:
Art. 3:
“If the employee joins another pension fund, the previous pension fund must pay the exit benefits to that new pension fund.”
→ If the employee changes jobs without a delay, there is no leeway for them to decide that some of it should join a vested benefit account, the whole exit benefits have to be transferred to the new pension fund. The obligation falls on the previous pension fund but the employee must give accurate information.
Art. 4
"If the employee doesn’t join another pension fund, they must notify their pension fund on what admissible form they intend to maintain their pension coverage.
[…]
If the employee joins another pension fund, the entity holding their vested benefits transfers the vested benefits to the new pension fund so as to maintain coverage. The insured person notifies:
a. the entity holding their vested benefits that they are joining a new pension fund;
b. the new pension fund what the name of the entity holding their vested benefits is and how they are held."
To sum up:
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All 2nd pillar assets must join the new pension fund whenever someone joins them (gets a new employer).
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The actual obligation falls on the previous pension fund or the entity that is holding the vested benefits.
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The employee must diligently and faithfully inform both parties so that they can execute on their obligations.
There is no legal grey area on the matter: whenever one is insured in a pension fund through their employer, all assets must be transfered to that pension fund. No vested benefits can lawfully be kept outside of it.
The question of how it is enforced and who will actually know if you willfully don’t perform your information duties is another question, and may be qualified as a grey area. The global answer, to me, would be:
Q: Am I allowed to keep part of my assets on a vested benefit account if I am employed?
A: no, you have to notify the entity(ies) holding your pension assets with information on your new pension fund and they have to transfer the assets to the new pension fund in full.
Q: Who will check if I am lying or willfully ommiting to inform a party I am legally bound to inform of my actual employment situation?
A: Asking the question is showing intent to voluntarily act beyond the law → that is not something I would expect to be discussed on a lawful open forum operating under Swiss law.