It’s possible to extend Bokeh with entirely new models, as you have seen. However, there is no mechanism to extend existing models, and in particular, Scatter has all of its marker types “baked in”, so to speak. You could subclass Scatter and add your new marker, but you’d still need to use the add_glyph nethod to add your new SpecialScatter glyph to a plot.
All that said, if the image above is your only requirement, it looks like you could accomplish it using two existing scatter glyphs. Plot an "asterisk" scatter first, then plot a "circle" scatter on top of those.