Afaik there is not a limit on fulfillment services
It can be mistakenly conflated with location limits:
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Apps that stock inventory or fulfill orders for you are considered to be locations but don't count towards those limits. When you add such an app to your store, or when you first enable locations, the app is automatically added as a location.
This is an accepted solution.
Nick here from Shopify. Great question!
You can add multiple fulfillment services should you wish. It can happen that stores use multiple fulfillment services. But as @PaulNewton mentioned there is a limit on the number of locations a store can use. You can see the breakdown of plans and number of locations possible from my screenshot of the setting up locations guide below:
That is the main thing to keep in mind when using multiple fulfillment services. Let me know if you have any more questions about this.
All the best, Nick