Brutal honesty time.
You're in a very difficult position on this one. From one perspective, the best practice would be to tell you all of those domains should be shut down, not even 301 redirects. It's the only "ideal" clean-up of what could very well be deemed mass-scale spam.
However, doing so could literally wipe out a significant volume of existing SEO strength that comes from the links because there's just no way to know how those sites are or are not impacting the main site at this point.
Alternate option:
If there are pages on the rogue domains not on the main site, are those pages that "should" be on the main site when taking the "single site" approach? If so, those should be moved and redirects set up. And if that content doesn't really belong on the main site, those pages should be redirected to their parent home page or wiped out entirely.
In this scenario, you're communicating "there's only one site - it's the site we want ranking, and thus we've taken action to kill all the renegade content".
This is the option I would recommend if it were my client.
Except how can you determine all the other rogue domains out there? That would be important to the process.
I would personally also need to evaluate current organic search traffic to help decide what to do. Is the total organic based visit count significant? Or is it almost non-existent? Because if it's almost non-existent, as painful as it might be to do so, I would opt for the first action - killing off all the rogue domains.
As drastic as it is, and as much as some SEOs would say "get what value you can from redirects", it really is the safest way, long-term to ensuring the site doesn't get slammed by Google. And if short-term or even mid-term rankings drop in that process, my position is still "I care most about long-term goals with sustainability and stabilization critical long-term elements.
Whatever you consider doing, I would also explain all of this to the site owner, and have them participate in the decision making process in a way you can be sure they first understand the issues and then that they have no ability afterward to blame you for anything that takes place due to past methods that were obviously ugly at best and reckless at worst.
I'd also love to hear what others here have to say about this and what they would recommend.