They may not be willing to give you a work permit because:
1. they may really not know the law/procedure -scoff, unlikely but, give them the benefit of the doubt. Maybe they've worked like that in the past, no problems... for them.
2. a company has to earn a certain amount to earn the right to hire a foreigner. not every company can hire a foreigner legally. Maybe they have not applied -this implies opening their tax records to the Govt. and we know not everyone is keen on that.
3. Maybe they have maxed their foreigner hiring capacity. Even at that point when they are allowed to hire foreigners, it is not an infinite number.
4. to you, the per hour sum is very nice. If they are not willing to give you a work permit, it means they are not reporting the salaries to the tax office and hence, no taxes are being paid. even if they are, without a permit, you can't collect the reimburse and most of all, there is a paper trail to follow. If they report your salary, they also have to pay NHI, laobao and other details over there. Turns out very complicated for some English lessons.
I agree there is a possibility to add a second employer, but that second employer has to be willing to give you the necessary paperwork, ie work permit. Remember that on a common ARC, the work permit belongs to them, they can deactivate it any minute they want, it is not yours nor it lives on in your ARC. Your ARC is just a reference. Also, I think there are provisions as limitations on that second employer. search that topic well.