Enterprise Diamond and Gold on same computer

If they are the same version-year, likely Enterprise 24.0, you can't install them both on the same computer.

That noted, I don't think there's any reason to have them both installed. This is because you can open and use as many files as you want using your QuickBooks subscription, and the payroll subscriptions are associated with your company files, not with the QuickBooks installation.

Thanks for the info! With that in mind, in quickbooks the only option I have is to enable assisted payroll, do you have any advice on how to change that to enhanced?

If you have a company file open that doesn't have a payroll subscription, and you start to sign up, you should be given all of the options available. 

That noted, I had a hard time figuring out how to do that. Intuit seems to have changed some things in an effort to try to sell Online Payroll to QuickBooks Desktop customers, which makes no sense and would be a horrible solution.

Maybe now you have to buy it first and then add it to the file using a license key they'll send to you.

Try starting here: https://quickbooks.intuit.com/desktop/enterprise/payroll/

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Edit: Actually, it looks like it's worse than I thought. It seems Intuit has tied the payroll subscription to the flavor of Enterprise, which is really very weird. If so, I don't know what they are thinking. Perhaps that's what you're seeing. Maybe if you call you can figure out how to just add a payroll subscription to your company file.

@kariham22 

You have an Enterprise Diamond license to manage 6 company files. How many company files do you currently need to run payroll?

Of the six, two have an active assisted payroll subscription. I have an additional company that needs to be enhanced payroll since we are paying employees in Wyoming and only enhanced can support that.

If you have Diamond Assisted Payroll, you can add up to three federal EINs. You don't need to purchase a new license for Enterprise Gold for the third company.

https://quickbooks.intuit.com/learn-support/en-us/help-article/payroll-setup/add-ein-existing-payrol...

I’m seeing that now from previous replies but now I’m wondering can I have enhanced payroll under the diamond level while keeping the other two at assisted? 

As I know, you're not allowed to downgrade from Assisted to Enhanced in Diamond. I recommend purchasing a new Enterprise Gold plan from a reseller, where you can get a discount of >20% to reduce costs. Then, you can consider purchasing a new computer or having a hosting provider to run it on the cloud.