In principle, fusion can continue beyond Carbon and Oxygen. However, such advanced burning in stars

1. Requires higher and higher temperatures because of having to overcome larger Coulomb barriers.
2. Produces less and less energy as the masses increase.
3. Cannot produce energy for fusion products beyond the Iron region (A~60) because that is where the peak of the binding energy curve is located:

Curve of binding energy.

In these more advanced burnings the mechanism is more complex than simple fusion. Typically the sequence involves the disintegration of nuclei by high energy photons in the plasma (a process called photodisintegration) and the subsequent recombination of these in a sequence of fusion reactions. This entire process is called nuclear statistical equilbrium, and is probably resposible for the production of elements from Neon (Ne) up the Iron (Fe) in stars.

We will have more to say about advanced burning stages when we consider late stellar evolution and the death of stars.

Information supplied by: http://csep10.phys.utk.edu