Have 30 amp circuit breaker (#10 wirer) to cook top. New cook top needs 40 amps.
Can I add a 20 amp circuit (#12 wirer) to the #10 wires coming into the new cook top to meet the 40 amps required?

Absolutely not.
You need a new 40A circuit run.

Several code and safety rules prohibit this.

Although your solution sounds good from a wallet standpoint, its also a good way to burn down your house with the new stove too. 4 wire #8 most likely needed.