I am using two map objects in QGIS print composer. One of them should be in WGS 84, being an overview of North America. The other should be in MTM 5 (close-up of a region). I can specify the projection in project properties but that sets the projections for both map objects. Is it possible to set the projection for the map object itself? (using QGIS 2.18 but could switch to 3.0)
It's not possible to my knowledge if using QGIS 2.18. You need at least 3.0 to do it.
The solution illustrated below
There is an article about this from @underdark e.g https://anitagraser.com/2018/01/20/freedom-of-projection-in-qgis3/