First, yes, it is possible to have more than one parasite.
Second, I would recommend taking an expectorant (cough medicine, but Not a cough suppressant) to help the stuff in your lungs come out easier.
Then I would want to know if you are taking some substance to cause a die-off.
(ANY change in diet at all.)
Then I would say start taking a magnesium supplement which will soften future BM's.
Then I would say, as fun as it sounds, grab some forceps and go fishing. If you want to find out what they are, either stick them in a plastic sealed container and send to a lab that analyzes stool samples, or you gotta take em apart yourself. Wear gloves and a mask, and treat it like haz mat cos it is, even if it's just last nights dinner. Dissect them on top of a plastic bag, outside, so you can throw away without dragging it all over, potentially spilling it, once you're through. Take pics and notes.