Elizabeth,
You can still have a closed system a-line even in one that needs to be opened up for blood draws. I wish I had the luxury of some visuals here, but alas I will have to rely on only my writing skills to give you the picture. I'll apologize in advance for that.
I'm guessing your current system has, from patient to monitor: the catheter in the artery, the line attached to that, a long line going to the transducer, then some tubing going to the pressure bad and another cable going to the monitor. In the middle of that long tubing that connects to the patient is usually a shorter piece of connector tubing with a three-way port/stopcock. Is this correct? Is this your current system?