Are you using your own custom basemap or one of the ArcGIS Online basemaps? the AGOL basemaps will only go down to level 16 or 19 depending on the basemap you are using. If you need to go down further I would recommend you swap out the AGOL basemap with one of your own map services.
It's actually REALLY easy with tilepackages. You can create and test them locally in Desktop and then publish the tilepackage to AGO as a hosted service. The tilepackage for a basemap covering the City of New Haven at 1:1128 took about 30 minutes to package and came to about 200mb. Publishing it has used virtually no credits. If you are going to cache it to collector, it probably won't use much in bandwidth credits, either.