Suggest Treatment To Get The Phlegm Out Of The Chest

My 81 years (young) old mother had a stroke 2 months ago and was paralyzed on her left side. She is currently in a nursing home making great progress and we are hopeful she will be home within a month or so. Although making progress, she has had a very hard time getting phlegm out of her chest and it keeps her up at night and also, when she eats her meals, has coughing fits due to the phlegm. You can hear/feel the rattling in the center of her chest. The Dr. say her lungs sound clear so there is no pnemonia present. They have her on an expectorant which is doing little to no good. It seems to be loosening it up a bit but is not helping her to get it up at all! She is feeling exhausted from coughing so hard and so often to no avail. Any hints/tips on how else to get it up? Thanks so much