You can't add to vector tile layers without republishing the entire thing. But you can always re-style your tiles after the fact. In my opinion, it's a good idea to put more data than you think you need into your vector tiles, then use different styles to highlight or hide features later.
Not having access to the source files, you could just publish your added layer as its own service, then configure your basemap to layer the two together. As long as your new layer is okay to be above every feature in the basemap, it will have the same visual effect as being in the basemap itself, just a little less efficient.
- Josh Carlson
Kendall County GIS