Concurrent H-1B for Part Time Job

I am working for company X as a full time employee on H-1B visa. They have filed my green card and my I-140 has been improved. Company Y to hire me as a part time on W2 but I need to work as and when required. So sometime I have to work 20-3- hours in a week and sometime, I will not have work for months. I can work from home too during off hours. Company Y is going to file concurrent H-1B. I have few questions regarding my visa:
1) Will it affect my current full time H-1B with Company X
2) Will it affect my green card process
3) Is it ok if I don't work for months for company Y without affecting Company Y's H-1B
4) If I get new I-94 through company Y, will it affect my current status?
5) Will company X know about H-1B filed by Company Y?

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ANSWER: 

This is not likely to work. Filing a concurrent H-1 is perfectly acceptable in this case and it does not affect your green card process, nor your current H-1. I dont know of any way an H-1 can be approved for an intermittent employment.

Nonimmigrant Visas: 
Unless the context shows otherwise, all answers here were provided by Rajiv and were compiled and reported by our editorial team from comments and blog on immigration.com

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