There are services aimed at e.g. PR departments for enterprise that do something a little like what you've described. I believe https://hootsuite.com/ https://

There are services aimed at e.g. PR departments for enterprise that do something a little like what you've described. I believe https://hootsuite.com/ https://hootsuite.com/ is this sort of thing, but I haven't looked into it myself. I don't know how well it integrates into your actual "own site". edit: also https://onlywire.com/ https://onlywire.com/ seems to be the same sort of thing. I've just found these by Googling, though.