Adding overhang without a purpose (such as covering the actual cabinets, or for seating) is an expensive mistake. If you have larger cabinets and need a larger countertop to cover them, or are adding a 15" overhang for seating, then it's worth doing. You still need to keep in mind the necessary aisle widths needed and 42" is "standard". Some people get by with 36", but that's the smallest between counters that code allows. That means your cabinets should be at least 39" apart.

The purpose would be adding some real estate on either side of the cooktop. I only have 10" now.

But the overhang you add will have no logical relationship to the cabinets underneath. It will just be "extra" that will look strange and only give you a couple of inches at most. A better strategy would be to look at the overall layout with the goal of moving the cooktop off of the island.

I have seen overhangs on islands that don't have cabinets or stools underneath that look fine. It could also allow for some shallow shelves in that area - which I wish I had space for in my island!

The extra workspace on top would be worth it. Whether or not you want to deal with the disadvantages of a cooktop on an island is another issue. The saving money part would rank high on my list!

If you have the space, I'd extend the counter to have more space behind or even to the sides of a cooktop. It's a safety issue. If you think the overhangs look odd with nothing under them, put in some open shelving for cookbooks or knickknacks.

3 1/2" (1 1/2 of "normal" plus the 2") of overhang would look strange, and it doesn't offer enough room for anything useful. Even shallow shelving needs to be at least 6". The side where you can get 8" would offer that shallow shelving possibility at least, but I'm in the camp that says to look at redesign. It is probably less costly than you think, simply because of the cost of the island venting. You can easily and cheaply vent a cooktop on an exterior wall and use standardized appliances, which, again, are cheaper. If you're replacing cabinetry and appliances, moving the cooktop to the wall should be fully explored.

I extended the sides of my island 4 3/4 inches on both sides of my cooktop and it is wonderful! What a difference! The 4 3/4 inches is filled by small cabinets facing perpendicular to the cooktop - - can't remember the exact name of the type of cabinet - -that I hope to turn in to spice racks on either side of the island. The cabinets measure 4 3/4 inches deep and have functioning doors. I included the depth of the door in my measurement.
The extra space on both sides of the cooktop is a godsend!

I love my island cooktop! Wouldn't ever want to move it.

The entire remodel was driven by me wanting the cooktop out of the island. However, after further thought I realized that one problem might just be that I have a side by side refrigerator and need a single door opening to the counter beside it. Currently, the placement of the side by side leads to things like sandwiches being made ON the cooktop because that is the only place to sit things when they first come out of the fridge.

I've been following the "island your in cooktop or not" thread. Everyone has some good ideas and gave me some things to think about. I realized that I don't want to cook facing a wall; I had never really thought about that before. Every other configuration makes my work triangle too large. Then I had the epiphany of perhaps the main problem with the functionality of my kitchen is merely the refrigerator door swing.

I"m just trying to look at all my options. Plumeriavine, I would love to see a picture of your island!