My husband (Jim/IBM) has issues with phlegm also, when eating if he chokes and sometimes in the night if he starts coughing. We think the throat muscles are affected by the IBM, which makes both eating and coughing effectively, difficult. There are some medications like one of the liquid Tylenol's that contain an expectorant called guaifenesin. It seems to calm the throat and helps him sleep through the night. On a practical note, he drinks a liquid ensure type drink every day and uses the empty containers to spit into. I can throw these away each day. The only time he didn't have the phlegm was when he was on a peg tube and not eating by mouth. He's been able to eat real food (carefully) again now for over a year but does have to deal with the choking along the way.
He's enjoyed some outdoor parties this summer and what he does is: Eat at home first, then if there are foods he might like at the party, I'll stash some in the guest's refrigerator and take them home where he can enjoy it without worrying about choking in a group setting. I'll carry along a plastic plate with a cover for this and also one of his sippy cups (lightweight plastic with a lid and straw) so he can have a drink at the party. I hope these ideas might help others with IBM.
-Diana