can I have two part-time jobs with more than 20 hours per week?

I have a long-term resident visa and have no job restrictions. right now, I work part-time, averaging more than 20 hours per week. this means my current workplace pays for my insurance, pension, and taxes. but I want to start another part-time job, mostly because of the industry that I wish to try. I want to work here more than 20 hours too. I know about the limitations of 40 hours per week, so I was planning to juggle my jobs: this week twenty plus hours here, next week there. I’m not sure if it's possible. Also, I’m not sure what will happen with medical insurance and pension, because if I work more than 20 hours, the company has to provide them to me. but how can it be managed, if I already have it?

I wish to hear someone's experience or how it is supposed to be. If it's important, one job is in Tokyo, another one in Chiba. my current company doesn't have any restrictions on my other possible workplace.