It depends on the individuals involved. Most of the time it works out fine as long as the chicks are within a couple weeks in age, but you don't want to attempt any additions after age four weeks.
When adding day-olds it helps to place them with the older chicks with a see-through barrier to protect them until they adjust and begin to know and learn the behavior of the older chicks. Chicks right out of an incubator don't have the experience yet to cope, but by the end of their first week, they will probably be ready to try mingling with the older ones.
It's not always the case that the aggression will come from the older chicks. A poster recently had a thread on here where the two-day old was the tyrant bully, jumping on and attacking the older chicks.
I have an article on how to cope with bully chicks linked below under "Articles".
We had a younger chick that severely bullied our bigger, older chicks. They only had about a week between them, age wise. It was the weirdest thing. Maybe it's not super common, but this baby chick was terrible. Injured all of the others within half a day to the point where they had multiple bleeding injuries each. Tried to separate and re-integrate (chick rehab!) with no success, so she was re-homed. Her sister (who we just found out is actually a roo) never had any issues being brought into the flock with the age difference. She was treated the same as the other birds immediately. I guess it just depends on your individual birds.
We have three 1 week old Easter Eggers that we're integrating with our 5 weekers. The older chicks aren't really interested in them until I put them in the run together for short spurts and then they want to peck them. So it'll probably be a few weeks before the hardware cloth that separates them can come off.
I recently successfully added a couple-day-old chick in with 3 2-week-olds. I did keep them separated by a wire barrier for a few hours.
Now, I say "successfully" but it was my chick mentioned above who turned out to be a baby bully! Some poke therapy ensued and all is now fine, but I certainly needn't have worried about the little one taking a beating.