Hi, yes, like the others said there is room. However egg size will determine how well you will be able to tip them side to side within the egg carton cups. Smaller eggs and silkie eggs are no problem, but tall, oblong, or XL eggs are a challenge. The newest version of the 360 doesn't really have the room to tilt the entire carton side to side...I tested it with my plain eggs. But maybe if you cut the carton in half so they fit towards the outer ring it might work. One person I know tiled the entire incubator side to side and said she had to keep less water in it that way, but overall doesn't think it (tilting the NR360) helped any.
I just had a shipment of eggs come in and anticipated that all might have to be upright, so I cut up toilet paper tubes and tested those out. If you cut them at a slight angle, maybe an inch high, they can hold large eggs upright/at an angle nicely and you can twist or turn your eggs however you wish.
Ultimately I decided only one of my shipped eggs needed to stay upright, but not all of them, so I made a little cradle that attached on top of the turner for that particular egg.
Remember coloring Easter eggs? How after you dye them you put them on a little piece of cardboard with circles cut out to hold the egg whole it dries? That's what I did. It needed a counterbalance on the opposite side to keep the turner level and rolling smoothly, so I set one from my flock.... about the same weight.
So far so good.