I had this problem, magnified - when I wanted to have the old carpet in my Living room and Hallway all taken up and a Laminate floor laid there.
Firm (Local) that I used said that provided I empties all the storage units and cleared as much of the smaller furniture as possible, they would work around the rest.
I spent seven weeks, slowly packing everything up from all those units and storing all those boxes in my spare bedroom. I was fortunate that my bubble family came over day before work was due to start to help take out all the smaller furniture and set me up with an armchair, etc in my bedroom to act as a bedsitter whilst this work was carried out.
The men then piled all the other furniture up and worked around this. It was a three day job, and I found it all highly stressful. I even stored a whole lot of stuff in my bath, to get it out of the way. Fortunate, I was able to keep clear my en-suite shower room.
Then my family came back to return all the furniture to its proper place to let me unpack.
I do want to have both the bedrooms re-carpeted and would use the same company, but have told them that I will need a good year to recover from this upheaval, and then to have further upheaval with the bedrooms.