The short answer here is no, you can't do what you are asking with the existing file permissions system. Delete will require write access, and even the sticky bit on the directory will only prevent deletes/renames by non-owners, there is no reverse equivalent.
I suppose there might be a way to do this with FUSE but that would be a lot of work - if you are going to go to that sort of trouble, an application to control access would be a lot more flexible.
Finally, if this is simply about changing/updating/removing files, I would probably use a version control system like git to allow someone to change whatever they like on their local copy but then have to submit a pull request (or get permission to check in etc.) their changes to the master copy. It requires a workflow change but gives you nice ways to roll back, reject changes etc.