.. for example, the Enterprise could have a malfunctioning turbolift and a malfunctioning Hydroponics lab…

A: Yes, you could have a piece of equipment which has multiple Malfunctions, just as in the example you provided (nice!) And, since they would be different breakdowns, yes, as you have hypothesized, the Engineer could only fix one on your turn, and then you’d have to wait for your turn to come around again for them to fix the second one.