Site #1
The first site I found is alvarotrigo.com, where they focus on the animations and end results on the hamburger menu icon when clicked on. While some hamburgers turn into X's, to signfy that another click will close the menu, there are a couple examples listed that do change the hamburger to be an arrow that points in a specific direction, which could be useful for some websites based on the existing layout.
Website Link: alvarotrigo.com/blog/hamburger-menu-css
Site #2
The next site was codemyui.com, where everything was focused on how the menu displayed and animated on screen when the hamburger menu was clicked. There were many options from a little sidebar appearing on the page, to a small menu hovering below the hamburger icon, to an animation playing that opened up the menu to the whole screen.
Website Link: codemyui.com/tag/hamburger-menu
Site #3
The last site I looked at was dev.to, where they provided some examples that were similar to both websites already looked at. There were several examples where the main focus was placed onto the actual animation of the burger, while others focused on the menu that appeared afterward. In addition, there was also a menu example that used a hover feature rather than a button, where the user could hover their mouse over a certain portion of the screen to be able to open the menu, then hover away from the menu to close it again.
Website Link: dev.to/webdeasy/10-awesome-css-hamburger-menus-1iho
Summary
To summarize, there are numerous ways for the hamburger menu to be modified, as well as the menu that comes from said hamburger menu icon. There are also a lot of online resources out there that can provide you with the CSS and HTML code necessary to recreate these into your own website to use.