If I remember right, the Michigan corpora (MICASE and MICUSP) had a way to set for non-native speakers. https://lsa.umich.edu/eli/language-resources/micase-micusp.html
I know we used some other corpora in grad school but I'm not remembering off-hand. I'll look through my notes when I have time.
I did a quick search for learner corpora and found this: https://uclouvain.be/en/research-institutes/ilc/cecl/learner-corpora-around-the-world.html
It's a list of learner corpora (for a variety of target and native languages).