Wisconsin is a multi state with several other states regarding your license. For example, it is a multi state with Iowa so you can go work in Iowa with your Wisconsin license as long as you retain living arrangements in Wisconsin. However, it is not a multi state with Illinois. Illinois is a tough state to get a license in. It generally takes a few months. So if you are thinking of getting a license in Illinois I would begin working on it now.
I would recommend calling the number on their website. You may be on hold for a while, but they will at least send you the important forms that you need to fill out and you can avoid dealing with the confusion on the website.
Add getting IL to endorse your license to another state to the list of things that take forever. I sent my $ and request to them over a month ago, for endorsement to Florida & they've yet to make any progress. This is the only thing left before I can get the FL license. Argh!