is it possible to OVERTRAIN while crosstraining

Yes

it is possible to over train doing any form of exercise if there are too many high intensity efforts.

any high intensity exercise that calls on adrenalin will raise cortisol levels which is catabolic to your body and will quickly lead to burnout.

You can definitely overlrain and you can easily get an overuse injury. On the elliptical you're standing in the same position for long periods of time, it can be really taxing on your posterior tibial tendon because you aren't moving through the same range of motion as with running. Depending on how long you're out for, maybe consider mixing it up more with cycling and swimming./ aqua jogging. Good luck!

I've done moderate to high intensity elliptical for anywhere from 3-10 hours/week consistently for the past 20 years without any issues. It's a great way to get volume and intensity in without the injury risk of higher impact. Good luck

It's possible, but at the same time if you listen to your body you can go a long way on the elliptical.

The recovery from the elliptical is much faster than running and I think hard workouts on consecutive days is doable if you feel up to it.

I once used the elliptical for 80-120 minutes a day for 6 weeks straight. I went hard whenever I felt like it. No injuries or aches and pains from it. When I resumed running, I got back in shape very quickly.

I think the answer is common sense. That being yes. Anytime you do an activity that your body is not use to you run a greater chance of getting injured than running.

Yes to the titular question. It’s called overcross training wherein you cross over to the other sport.

A common phrase and triathlon training is that you can over train in three sports just as easily as you can over train in one.
try alternating hard elliptical with long elliptical. over training is more likely when you get the heart rate too high too many days in a row. Less likely to have happen if you go long and easy.