I would go back to them and ask them why they wouldn't just add a section to their existing website to cover the new multisites multitechnic maintenance activity.
Option 1
If you use a sub domain or a concatenation of it as you have shown with the hyphen it simply looks bad from a URL perspective. One could argue that visually it is very spammy. Remember in the not too distant past you would have domains like www.the-best-maintenance-contractor.com (I made that up!) ? - It just looks unprofessional.
Option 2
The second option - to set up a new brand involves much more than just buying a new domain. There is a whole host of branding issues and SEO problems to consider:
No Domain Authority
New Logo
New Stationery
New Socials
New Email Addresses
New Google Tools etc etc etc
Plus the fact that a new brand name and URL can take a year to properly proliferate and find its optimum position in Google. You would effectively be starting from scratch.
Option 3
My preference in this case would be to use a folder for the new activity vis:
Then use sub categories of that.
myccompany.com/maintenance/activity1
myccompany.com/maintenance/activity2
etc
This will achieve much better results in SERPS as the company already exists and presumably already has Domain Authority.
You just need to tell them.
I hope that helps
Nigel