I think PUT is only used on an Entity not on a Collection
No - PUT is used on a resource, not on an entity or collection.
The PUT method requests that the state of the target resource be created or replaced with the state defined by the representation enclosed in the request message payload.
The changes that happen to the entities in your domain are a side effect of the manipulation of REST resources. See Jim Webber's talk REST: DDD in the Large.
If your message body is a replacement representation for the resource, then either POST or PUT is the appropriate method to use
If your message body is a patch document, then you should use POST or PATCH.
If you are concerned that POST would be overloaded, then create a new resource in your design to manage this part of your integration protocol.
Again, heed Jim Webber:
URIs do NOT map onto domain objects - that violates encapsulation. Work (ex: issuing commands to the domain model) is a side effect of managing resources. In other words, the resources are part of the anti-corruption layer. You should expect to have many many more resources in your integration domain than you do business objects in your business domain.