You may not need to go through such provincial nominee programs. You would probably have options, but it depends on many scenarios. For instance, the size of your current business, your intention on a personal level where you wish to spend most of your time, if you wish to bring key personnel with you, etc.
As a U.S. green card holder, how can I set up a business in Canada?
I own a trading business in the U.S. and would like to expand it to Canada. I am a U.S. green card holder. Do I need to go through the provincial nominee systems as a regular immigration investor, or are there any special treaties between the U.S. and Canada, which would allow me to establish a company in Canada as a green card holder?