Yes, a handyman can advertise multiple eligible services through one LSA profile without creating separate accounts for each trade. The services need to fall within the business categories and job types Google allows for that business and location.
For example, a handyman may be able to promote services such as minor plumbing, drywall repair, painting, or carpentry through the same profile, depending on what is eligible.
The important part is to list only services the business actually provides. Adding too many unrelated services can bring in leads that are a poor fit.
If you offer several trades, review which services generate qualified leads and focus your LSA setup and budget on the ones that bring in the best customers.