X is in the US in H1b status (See 8 USC 1101(a)(15)(H)(i)(b)). The H1b authorization is per employer (including self, if it wasn't clear initially to some people), see 8 USC 1184(c). So if X takes employment with another employer, they'd must go through another authorization, see 8 USC 1184(n)). This is a condition of their status. The location of the employer doesn't matter, what matters is the location of work being done (in fact, the H1B LCA is specific to a location, and even switching offices within the US with the same employer requires some paperwork). So it doesn't matter if the other position is with a Singaporean or Swiss employer - if X is doing it while in the US they need another H1b authorization.
See 20 CFR 655.730:
(5) Multiple positions and/or places of employment. The employer shall file a separate LCA for each occupation in which the employer intends to employ one or more nonimmigrants, but the LCA may cover more than one intended position (employment opportunity) within that occupation. All intended places of employment shall be identified on the LCA; the employer may file one or more additional LCAs to identify additional places of employment. Separate LCAs must be filed for H-1B, H-1B1, and E-3 nonimmigrants.
(6) Full-time and part-time jobs. The position(s) covered by the LCA may be either full-time or part-time; full-time and part-time positions can not be combined on a single LCA.
If your intention is that X performs all their duties for the part time employer outside the US, while working full time inside the US, then legally they should be fine without an additional work authorization (given they do in fact comply with such a separation and have a proper work authorization in the other jurisdiction), but practically this sounds implausible.
To address some critique in comments:
- Second job must not be "independent contractor", there's no such law in the US that mandates a single employer at any given time and plenty of people have multiple jobs.
- Claiming you're an "independent contractor" doesn't miraculously exempt you from work authorization requirements. The INA sections I refer to say nothing about employer when demanding labor certification and employer petition, and self-employed people have an employer: self.
- A lot of people have a lot of strong opinions on things they don't understand, that is our sacred right as Americans. When in doubt - hire a professional legal expert (a lawyer licensed to practice in your State), and don't rely on random answers on an anonymous Internet forum.