When I zoom in , Web Mercator is no longer suitable, I have some X/Y data that I need to overlay but is distorted in Web Mercator. I
need specific projections for our work areas.
If you need to use specific projection, you should create the whole mapview/map using that projection from the beginning. ArcGIS Online is publishing basemaps in WGS84 so you need to use other basemaps (hosted either by esri or other entities) with your local projection. When you are setting first layer into the map, it's spatial reference is used in a map if it's not explicitly specified. You can find more information here.
Thank you Antti for responding! Unfortunately the link "here" for more information, is broken. May I impose on you to check that link or alternate as I would really like to follow that.
Thanks in advance.