Are there any concerns about using nintedanib in a patient with progressive fibrosing ILD on background mycophenolate?

The SENSCIS trial randomized patients with SSc associated ILD to Nintedanib or placebo. I think about half of these patients were still taking MMF. There was no negative signal in the group on MMF and Nintedanib, they fared at least as well as those who got Nintedanib alone and both did better than placebo. Thus, unlike some of the data in IPF (PANTHER-IPF trial) suggesting worse outcomes with AZA/prednisone and pirfenidone, it appeared to be safe in this very limited population. 

That being said, I would point out:

1. Senscis enrollment required only radiographic evidence of fibrosis without any need to show decline in FVC, DLco, or progression of symptoms. Thus, these patients didn't necessarily have PF-ILD. 
2. The follow-up to this study was the INBUILD study which broadened enrollment to all forms of non IPF ILD. Most patients had either CT associated ILD or chronic hypersensitivity pneumonitis. They did require patients to have a decline in FVC of > 10% in 24 mos OR CT or symptom progression and 5% decline in FVC> OR both CT and symptom progression. So these patients did have PF-ILD with what is considered accepted diagnostic criteria (although not validated). Unfortunately, they did allow patients to be on immunosuppression with the drugs we use for ILD, thus it does not answer your initial question. 

We have been using it in our practice though with some trepidation. I have seen it being prescribed frequently for patients by our local rheumatologists, however often those patients have not been screened for PF-ILD. I don't think one should use it for newly diagnosed patients whose PFTs are declining prior to receiving treatment for their inflammatory lung ds. It should be reserved for those who fail to respond and continue to progress.