Signature PDF is a free web application for signing and editing PDF files. You can add a signature, initials, a stamp or text, either alone or together with others through a shared link. It also lets you merge, reorder, extract and rotate pages, edit metadata, recognise text with OCR, add a watermark, redact areas of a document and compress files. It is used in the browser and can be installed by an organisation itself.
The software is maintained by 24ème, a French company in Paris that develops free software; all code the company produces is released under the AGPL v3. According to the documentation, you can install Signature PDF on Debian, Ubuntu or Alpine, or with Docker. Storing documents for signing by several people is optional, can be encrypted with GPG and has a configurable retention period. Because you can run the application on your own infrastructure, documents do not have to leave your environment. Besides self-hosting, 24ème and other organisations run public instances; how data is handled there is decided by the operator of that instance.