I might get corrected here, but as I understand it, the current theory is that all surviving Rossington families are related. (There may have been others which died out.)
This makes the Rossingtons particularly interesting for a Y DNA study. Y DNA is the DNA which only gets passed from father to son. Women do not have it. There are now at least 3 labs who do profession genealogical DNA tests. For genealogists, they only test a few unimportant parts of the DNA, which change relatively quickly. What the results do is allow us to re-check branches where the connections are not certain.Some possibilities will be shown impossible and, judged by the experience of some surname projects (try Google and look for some examples), some surprising new links will be shown to be possible. In my own case, where our branch descend from a Rossington mother who gave her own name, it will first of all give future Rossington genealogists a reference to know whether they are from my branch or not, and secondly it will help find out who the mysterious father was.
The best company for helping coordinate a project, whereby everyone with the same surname can have the information collected by a central coordinator, seems to be FT DNA. I am also using them for my own surname after getting involved with another project for my mother's mother's surname. (Rossington is my mother's surname, so I have to find an uncle for example, for this test.) Search for FT DNA with Google. I have already had confirmation from them that we can either start a project before we have any results, or if various Rossingtons get their own tests done individually first, they will be happy to allow us to put together a project afterwards.