QB Issue Resolution:

Unlike QBO where you have to pay for each company/subscription, with the desktop versions you may create as many companies as your hard drive will hold. Only with the accountant’s version may you open 2 companies at a time (the second with somewhat limited capabilities). However, if you have more than one version of QB (e.g., QB Pro 2014 and QB Pro 2015) you may have both open at the same time.

Resolution for Issue 'How many business accounts can I manage on QB (online vs pro)? Unlimited?' available: Yes (Solved).
Source: Intuit Community forum.

How many business accounts can I manage on QB (online vs pro)? Unlimited?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

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