I'd like to have a tool (software or website) that helps me in doing literature surveys. Here's how I pictured that tool in my mind. Let's suppose that I've found myself a few relevant papers. As soon as I feed such references to the tool, it starts suggesting me other papers I might be interested to. Suggested references could be paper that are cited by several papers that are already in my bibliography, or papers which cite several entries I provided. If I find something interesting, I could "swipe right" (if you get my Tinder analogy) and that paper is added to my bibliography. The more paper I have in the bibliography, the more fitting the suggestions of the tool become. Of course such a tool should rely on an existing database (Scopus, google scholar, etc.) Do you know anything like that?
As well as Mendeley, for Biology and Medicine people there is also PubChase, which does exactly what you say you are looking for. How well it works I couldn't say. It always has interesting suggests for me, but I wouldn't rely on it to be comprehensive.
Although I don't use it myself actively, what you describe seems to be included in the social network aspects of Mendeley. Mendeley is primarily a fantastic reference management software (very similar in functionality to Zotero, which is what I personally use), but it additionally has a rich social component which seems to include recommendations of similar articles. So, it seems to both included the recommendation agent and reference storage features that you are looking for.
Another tool that partially has such features is ResearchGate (see the "Similar research" section when you scroll down below any article you look at). It has quite a rich recommendation agent, but not quite as rich reference storage features.