Adam, find out (if you can) what company manufactured the shed and go see them.
If you don't know who manufactured it, take some photos of it, including showing the framework (if any) and take the photos to a few shed sales places, they may recognize what it is.
Watch a few videos (youtube) on DIY assembly of prefab steel sheds, and see how they go together.
Absco is a popular brand of simple lightweight steel shed, if you watch a few of their DIY assembly videos, you will get some idea how they go together, and then if you think your shed is similar, talk to them about buying the parts to convert your single door to a double door shed.
I have one of the sheds shown in the video, it was no picnic assembling it, lots of things didn't line up as they should. You would want pretty good handy person skills, and the ability to solve problems as you go. Otherwise it could be a very frustrating experience.
Steelchief is another very popular brand, I think each wall panel on theirs are pre-assembled? So they are easier to put up, but more expensive.
These are simple frameless sheds, the steel wall panels support the structure without any wall framing, just stiffener rails top and bottom of each wall panel.
If yours is that type of construction, it wouldn't be hard to remove a section of the wall sheeting and replace it with an extra door.
It that is beyond your skill level, get quotes for a handy person or carpenter,or even a shed company, to modify your shed.
On the other hand, I would be questioning if this washing machine is really worth all that bother? It might be more sensible to just sell that over-size washing machine to someone who has the space for it.
