I was wondering if it's possible to see the schedule and buy the services of multiple providers
If you are looking to see the schedule of more than one provider, you only need to ask the new provider to invite you to their system! Accept the invite and you will see their schedule and offered services.
As shown below you can filter through the timetables of your fitness providers and you can choose to see the schedule of all of them or a particular provider.
Also, when buying their services (memberships/packages), you can see which service is provided by which trainer by looking at the bottom of every service: