If you want chewy cookies, add melted butter. Butter is 20 percent water. Melting helps water in butter mix with flour to form gluten.
More gluten will make for a chewier cookie, just as it will make for a chewier bread. Keep in mind that you're introducing extra liquid with a substitution like this one, and the cookies may be thinner than you'd like unless you add more dry ingredients or less liquid.
If you want thin, candy-like cookies, add more sugar. Sugar becomes fluid in the oven and helps cookies spread.
A little extra sugar will also help you get a crisp edge on a cookie. Caramelized sugar does not always survive well in the open air. Too much sugar and your cookies will be thin and chewy, not crisp, although they should still taste great. An airtight container will help preserve their fresh-from-the oven texture.
The same warning about too much liquid can apply to this. Too much egg and you'll have cookies that have an eggy flavor to them and a spongy texture. It's best to start with small additions, maybe one yolk or white at a time
If you want an open, coarse crumb and craggy top, add baking soda. Baking soda reacts quickly with acidic ingredients (such as brown sugar) to create lots of gas bubbles. If you want a fine, tight crumb and smooth top, add baking powder. Baking powder works slowly and allows for an even rise.
Leavenings interact heavily with the other ingredients in a cookie, so a small amount of baking powder or baking soda added may not make much of a difference. A cookie that is already tending towards cakiness, for instance, will be more likely to have a smooth top than a craggy one. You may want to try two batches at once when experimenting with leavenings so you can easily track your progress.