Nobody fully read the question.
OP says to assume it’s the patient’s own, predonated blood.
Well, if you’re going to get continuous pints of blood, you have to be continuously bleeding - internally or externally - to justify the IVs. (I doubt that a doctor would order blood for someone who wasn’t bleeding. There may be exceptions, however, but I have never seen one.)
So, the pt.'s pressure wouldn’t go up. The transfusions would simply replace blood that was being lost.
Anyway…
There was an awful case of hemorrhaging when I was a night call lab tech back in the 50’s-60’s. If I remember correctly the guy had esophageal varicoses (varicose veins of the food tube), which ruptured. He bled as fast as I could get replacement blood up to the floors.
In the middle of the night, I hand carried two pints to the floor. This was a small ~200-bed hospital. When I stepped off the elevator, I could smell the blood pouring out of this poor bastard. Actually it probably smelled more like meat. I mean it hit with incredible force. It’s a smell I have experienced in an autopsy, but nowhere else.
We must have pumped 12 or more pints of blood into this guy before he died.
And if I may…
I’d like to put in a plug in here for the American Red Cross Volunteers. They’re the unsung heroes behind the scene. When I (and other techs) got into I NEED BLOOD AND I NEED IT NOW situations, I’d call the Red Cross. They’d scour the local hospitals for spare pints of the needed blood type and hustle them over to my lab. If that wasn’t enough, they’d line up emergency donors.
And when these people would come into the lab carrying that life saving fluid, they exuded an aura of goodness, of saintliness about them. Honest. Except for their “holiness,” they’d be otherwise very ordinary folks. And they had no pretensions. They didin’t think of themselves as a cut above anyone else. They were simply doing a job - for no pay whatever - that they knew was important.