I have a QB Self Employed account for my business. I am starting a second separate business, can I have another QB Self employed account alongside this one?

You can have a new subscription for the other business, info1342.

To register your other business in QuickBooks Self-Employed, you can have a separate subscription. When you subscribe to the program, we'll have to use different credentials. If you'll select the Sign into existing, the program will just route you to the existing subscription. We'll have to use your other email to able to successfully subscribe. 

I've added an article that will help you in setting up your second company in your new QBSE account: QuickBooks Self-Employed Overview. You might want to also connect your bank and credit card accounts to QuickBooks Self-Employed to automatically download your recent transactions.

I'm just here if you have other questions in mind. You take care and have a great day!