That doesn't make a lot of sense... having one less tag manager is better for performance.. why would they think adding a second one would help anything?
Assuming this works, which I don't know it even would.. there are general standard scripts that come along with the tag manager that would be loaded twice (for each script) which would definitely be detrimental to performance (and that's assuming having two versions of those scripts don't clash with one another). Not to mention, performance improves by having less individual resource calls.. so adding a whole new tag manager is opposite to that philosophy...
You can set different triggers in Adobe Launch, you don't need to fire everything all at once.... Adobe Launch is already generally loaded as an async script already...
If they are having issues with timing:
i.e maybe they are using DOM Ready, or Window Loaded to trigger the tracking, but not all the elements are ready, they can do what we did.
Our sites have a dependency on some slower third party "cross tracking"... so I had my developers create a custom JS event.. when the site loads, they can collect all the data we need for tracking, set it to our data layer, then they fire the custom event (screenChange).
My trigger in Adobe Launch is a custom code trigger that looks for "screenChange"... basically this is similar to how you would handle an SPA site (that only triggers DOM Ready or Window Loaded on the initial page, then uses JS to update the content of the page without actually triggering standard web loading events)
If you really wanted to, you could set up multiple events that trigger at different times in the page load cycle.