You should check with your lawyer, but if you mix the accounts, those funds may be vulnerable if one of the companies has legal action brought against it. I would create a separate account to manage those funds, even if the second company is a subsidiary of the original company. You should also make sure your company is properly registered (ie- Incorporated, Sole Proprietor, etc.)
Business account for each business is the way to go. You sound as if you are trying to economise and skip accountants and lawyers fees. realise now that if that is the case, stop business plans straightway because you are bound to lose everything you put into it. At least, ask your bank manger/accountant for an opinion.Good ideas and new business have a bad habit of costing more money than you ever get back from them.
Every EIN should have a separate account.