Invitation to Collaboration

Hi there, 

Welcome to Box Community and glad to assist!

Yes, you can accept multiple, different collaboration invitations. Is there an error message when you try to accept the invite?

To make sure all invitations will be accepted, please follow this process. 

To find and resolve a pending invitation:

1. In the left menu of your Box account window, click All Files.
2. In the pending invitations panel under ACTION REQUIRED, hover on the name of a file or folder.
3. To see details about the invitation, click the ellipses, "...", and select View Details.
4. To decline the invitation, click the ellipses, "...", and select Decline All.
5. To accept the invitation and gain access to the project's content, click Accept.

 For more details, please see this article. 

Thanks for posting!