I was going to start with the two flat, but a dearth of images, and more especially plans, stymied that plan. They will be covered ad nauseum in later posts.
Many three-flats follow the same basic plan of the two-flat, living room, dining room on one side with the bathroom and kitchen directly behind, off a corridor, and the bedrooms and stairs on the other side. Three-flats begin to vary this, with what I term the zig-zag layout, with the living room in front and the dining room behind the stairs - in this variation an actual entrance hall or foyer is also often provided. Then the kitchen can be directly behind the dining room of, completing the zig-zag in the other corner of the apartment, with a bedroom directly behind the dining room.
The plan above is a good example of this with the public rooms in opposite corners from each other (I include the kitchen in this). The bedrooms and bathrooms are fitted into this plan, and a nice touch, not accessed directly off of any of the public rooms, but from the foyer or back hallway.
The image to the right indicates this type well enough; this was typical in the teens more than any other era, and into the twenties, before the plan was refined into what many have called the golden age or era of apartment design (not just in Chicago, but nationally). A nice deep brick color and sparse limestone trim with heavy, solid porch columns make this a nice, discreetly elegant addition to any block. It also shows the waning craftsman influence which then flowered into a typically Chicago style of decoration, particularly on the bungalow, but also on multi-family dwelling as well. This one was not shorn of it's cornice like many, but has a minimal limestone coping above the third floor windows. Many of this type had a massive square projecting, protrusion like tin cornice, which I suspect was a stand, readily available product, cheap enough for developers of the era to be able to install and dress up an otherwise plain building. Unfortunately many of these have not been kept up and removed over the years - this was also done for aesthetic reasons in the middle of the last century when fussy ornament was out of style and older buildings were modernized (not the least for ease of maintenance).