You have two options, one is a complete service change. The average house service these days is 200 amps 42 circuits. The second option is to install a sub panel off the existing service. Depending on how many circuits you need will govern the size the sub panel. Here is where it gets tricky. Two side by side single pole breakers or one two pole breaker will have to be removed from the original service panel and replaced with a new two pole breaker. The size of this breaker will be governed by the total load of the new sub panel. The wire from the new sub panel to the two pole breaker is also governed by the load of the sub panel. As an electrician I would recommend that you not do it yourself but get a qualified electrician to do it for you. He would (should) take a permit out for the job and get it inspected.
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If your breaker box is full, you may need to add a subpanel to accommodate more circuits. Contact a licensed electrician to assess your electrical needs and make any necessary upgrades to your electrical system. Avoid overloading circuits as it poses a fire hazard.
You would need one 30 amp double-pole breaker in the breaker box for a 240V cooktop.
Your only hope is that someone wired the box not to code and that there are two wires going into the offending breaker. If you can't separate wires you can't distribute the load.
To replace a 15 amp breaker, first shut off the main power to the circuit box. Then, remove the cover of the circuit box and unscrew the old breaker. Disconnect the wires attached to the old breaker, connect them to the new 15 amp breaker, and securely screw it in place. Finally, turn the main power back on to restore electricity.
The symbol for a home run on a breaker is a box with the number "4" inside it.
You can determine the size of your main breaker box by looking at the number of circuits it can handle. A typical residential main breaker box is usually 100 amps, 150 amps, or 200 amps. You can also check the label on your breaker box or consult with an electrician for assistance.