Bluegrass needs full sun to grow. About the only grass that might grow in some shade is one of the fescues, but then the soil needs to be really good.

I was thinking about seeding the area with a blend of different fescue. The soil seems to vary around the yard, but is actually appears to be most fertile in the area where KBG isn't growing.

Paul

Most often what I see under trees where grass will not grow is a lack of enough organic matter to help the grass grow. The soil will be very compacted and the tree itself will suck any moisture from the soil leaving none for any grass, although lack of sunlight can also inhibit many grasses from growing. Contact the people at your counties University Of Illinois Cooperative Extension Service and ask about 1) having a good, reliable soil test done, and 2) which Fescues would grow well in shady areas. Then dig in with these simple soil tests,

1. Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
to see what that soil might need to grow a good turf.

I'd try fine fescues in the shady areas. Fine fescues are Chewings, hard, creeping red and sheep (but you probably won't see sheep fescue in a lawn mix). If you get a blend of fine fescues, get named varieties. Be careful not to get Boreal red fescue, because even though that sounds like it's a named variety, it's an unimproved type. There's a mix I've read nice things about called Bonny Dunes. If it's not available locally, you should be able to find it online, but you're pushing the timeline for a fall seeding in northern IL. You can dormant seed if you miss on the fall planting.

Many landscape people up here seed new lawns until the middle of October and those seeds germinate and grow before being covered with snow quite a bit. On occassion we have had snow fall, and stay, in early October but most of the time there is nothing much before mid November that might cause grass seeds from growing.

I would try something besides grass, a nice ground cover like jacob's ladder, native ginger, or woodland violets, makes a nice green alternative to lawn in those areas that are too shady to grow grass.

those plants do well under trees in my yard, they have to deal with not only the lack of sunlight, but the competition for moisture from the trees as well.