It completely depends on what jurisdiction the property is in. Every province and state has a different set of rules. In Ontario, for example, tenant/landlord interactions are governed by the Ontario Residential Tenancies Act. In Ontario's RTA, there are very limited circumstances to evict a tenant with the intention of rotating in a higher paying tenant. If you are substantially destroying the building, then you can use N13 reason 1. If you are renovating you can use N13 Reason 2 but the tenant has a right to first refusal (there is a procedure for the tenant to claim this). Alternatively you can offer cash for keys to essentially buy them out. You would use an N11 for a mutual termination.
Normally we just wait for tenants to turn over naturally unless circumstances force us to do otherwise. As such, we buy buildings with a tenant demographic that has a fairly high turn over rate.
In some provinces (e.g. Alberta), you can adjust rent to market at any time.
However you end up doing this, do try to keep an ethical stance. Consider what would be acceptable if you were a tenant in this situation. While it is a business, we need to keep in mind that, as rental housing providers, we are dealing with peoples' homes.