At any rate, there are a bunch in Montreal. Here's one: https://www.rocklandmd.com/en/medical-clinic.html Here's another: https://cliniquesmedicaleslacroix.com/en/ You can certainly find more by searching for "[Canadian Place Name] private clinic"
Heck, here's a news article about the Quebec government outsourcing some work to private clinics to clear COVID-related backlogs. For there to be $100M worth of contracts, there must be a decent number of clinics.
https://www.cbc.ca/news/canada/montreal/private-clinics-queb...
Doctors are not able to work in both the public and private systems, they have to choose.
There are a few clinics that provide care entirely outside the public system but since the demand is low they are rare beyond MRI clinics in a few provinces.
But please, send me links to the dozen of private clinics (dont work in the public system) that are 30 mins of where you live.
Demand used to be low, it is increasing steadily due to mismanagement.
If you don't trust me, type "private clinic toronto" into Google Maps.