what type of lawn are you trying to improve? I assume where you live, it is either zoysia, bermuda, or turf type tall fescue. If you core areate the zoysia or bermuda and properly fertilize it, it will fill in. Turf Type tall fescue is a bunch grass and will require seed. As stated the cross core areating will do a great job. I would suggest lightly rolling the lawn after you seed. The seed germinates the best when it has good contact with the soil. I spent many years in the turf industry and sold grass seed from the cool season grasses in the north to warm season grasses. Seeding many times is over complicated. Areate, fertilize(with a good soil test) press the seed to the soil in some way, and water, water, water.