[fjtorres]

One of the ways these firms operate is to buy wholly owned subsidiaries to take them public. Also, it is worth remembering that library ebook lending isn't the only thing Overdrive does, just their dominant revenue stream.
They are also ebook distributors for white label ADEPT ebookstores. A dying business, I know, but their Libby app is all over the place--well over a million installs on Android--so they are a viable candidate to add ebook sales to Libby and add a consumer business.

They have the visibility and back end capabilities to expand into ebook and audiobook retail and challenge Amazon. They could also look to pbooks to challenge Ingram now that Baker and Taylor is out of the trade book distribution business. Or, less likely, they mivht buy Ingram.

Also, if B&N wants to get rid of Nook or their pbook distribution system (as suggested by Shatzkin), KKR could buy it cheap and combine the three properties, run it a year, and IPO it.

They paid a premium for Overdrive so expansion and IPO is the more likely plan.
What remains to be seen is how they go about it.

This could get interesting.