You can have as many different (and separate) budgets in YNAB as you'd like.
To make a new budget → File>Create a New Budget
To open another budget → File>Open
It works much like documents in a word processor. You can open one, work on it some, go after the next budget, etc.
The instructions below apply if you have your budgets Cloud Synced. If you're using Legacy Sync (WiFi) then you only need to sync a new desktop budget to the mobile app in order to replace it. Please be certain to first sync the budget on the mobile app with the desktop budget that matches it to avoid losing any changes you made there since the last sync.
iPhone: Tap the menu bars (top left) then tap the budget name to get to the list of budgets.
Android: Tap the menu icon (three vertical dots) in the top right corner of the main screen, then tap 'Open Budget' then select the budget you'd like to sync.
To move money between the two budgets, create an outflow transaction in the budget where you are removing the money. In the case of a business budget, this may be an outflow categorized as payroll when you pay yourself.
Then open the other budget and create an inflow categorizing appropriately.