Is there a tool like the Open Science Framework that can be run on a private server?
Moritz,

Jeff here--I'm the co-founder and CTO of the Center for Open Science--developers of the OSF. First off, I'm happy to hear that you like the OSF. While this doesn't answer your question necessarily, you have a few options if you'd still like to use our service:

It sounds like you're interested in encryption of data at rest, which is something we don't yet offer for OSF storage, although all data is encrypted during transmission. Of course you could encrypt the data before uploading it, but that's probably not an ideal solution. With that said, Amazon S3 (one of the services we connect to) offers encrypted buckets (so you'd get encryption of data at rest in a cloud service), and we make that option available via the OSF. Alternatively, you could install Dataverse on your own server and connect that to the OSF. Owncloud and Gitlab connections are coming soon--both storage services you can also host on your own machines. These latter services don't offer encryption of data at rest, but they wouldn't be hosted in the cloud.

Depending on your needs re:storage, there are a few other options that I'd be glad to talk to you about. For example, I haven't tried it, but I think you could install the open source Minio server (which has an S3 compatible API) and connect to the OSF via our S3 add-on. We might need to make a few tweaks with regards to authentication, but we could look into adding that to the feature queue, or we always appreciate pull requests if you have developer time. You mentioned a donation, so if you did have some money for something like this, we could see if someone in the community would be interested in a bounty/grant. Alternatively, you could directly hire a developer or an intern to make the necessary changes and contribute code back to the code-base--making that add-on available to the rest of the community. 

So, lots of options, and we're happy to help support community-initiated endeavors like this. Feel free to get in touch with us at support at osf dot io or reach out to me directly at jeff at cos dot io. Hope to hear from you!