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Answer for Remote work options

You bring up a very common issue that so many employers are facing right now, employees that had hybrid work agreements or WFH agreements because of the pandemic that do not want to come back into the office, and in fact, want to explore the freedoms of remote work. Some employees are picking up stakes and moving to new Provinces, regions, or countries to minimize their cost of living. Is this good for employees and employers? There are benefits, but there are also some serious risks. 
Let’s put aside productivity issues, because employees can be unproductive in an office or a remote location – I firmly belive productivity is a behaviour and engagement issue and not correlated to location. Even those reports of employees working two full time jobs, both remote, is really about engagement, ethics, goals, and responsibilities – it may be easier to pull off this kind of “trickery” with a remote arrangement, but it’s really a problem with the person and not the work arrangement.
However, there are serious tax, worker’s comp, OH&S and payroll implications associated with remote, hybrid, and wandering employees. I recommend reading the following:

To specifically answer your questions… A) Yes you can differentiate and classify work arrangements as you deem appropriate, but keep it in writing. B.) As per A, yes, you as the employer can and should be the one setting the conditions of what is appropriate remote work, what locations are appropriate, etc. Employers are not obligated to accommodate an employee’s desire to work from home if it is merely a preference.