I'd love to know, too. We just had our lawn aerated and overseeded and I think I'd like to put down more seed specific for shade areas.

You can put more seed in bare areas now. It would not be good to put more seed overall. If you planted at the correct rate and then seed again, you could end up with seedlings that are too thick and don't grow well. The seedlings come in as thin plants. They will thicken up, especially after you start mowing. Mow before the grass is 1/3 more than your target height. Just be careful on the turns because the ground is soft. As for the shade seed, I suggest waiting. The seed you planted will grow for a while and if it doesn't get enough sun, it will decline. Probably by the late summer/early fall you will have enough bare soil to make room for the shade seed. Any cool season grass planted in the spring is going to struggle in the heat of summer and crabgrass will overtake it so be prepared to seed again in late August or early September.

You absolutely can overseed. Done with a clear field and all at once, you get a lot of grass plants competing for limited sunlight, water, and mineral resources. That tends to result in weak grass and disease, which will result in far worse conditions than seeding correctly would have given you.

Best case scenario, the stronger grass seedlings outcompete the weaker or later-sprouting ones. The excess seed was simply not necessary. But this is if you're lucky and no fungal issues move in.

Overseeding into a thick, established lawn is simply a waste. The adult plants can outcompete the seedlings effortlessly. The seedlings die.