You can do that already. Who says you have to count on the fingers?
Some cultures count between the fingers for a natural base 4 or base 8.
Some have counted between the fingers PLUS the outsides, giving you natural base 6 or base 12.
Others have counted the segments of the fingers which, at three per finger, gives you a natural base 12 one handed.
At least one culture counted the segments of the fingers and one past onto where the finger connects to the palm. That's a natural base 16. On one hand.