Can I purchase and run another of my companies on the same software that I currently own?

I'll help you sign up a new QuickBooks Online account, michaelparkes51. 

One QuickBooks Online account can only be utilized for one company. To add more companies, you'll have to sign up for more QuickBooks Online accounts.

Let me show you how:

1. Go to this website: https://quickbooks.intuit.com/uk/.
2. Select the version you'd like. 
3. Click on the Sign in link.
4. Enter your QBO login credentials. 
5. Click on Sign in.

You can now access your QuickBooks Online accounts using one login credentials.

You're always welcome to post more questions about QuickBooks. We are happy to help.