There are building regulations regarding stair construction, so you may be wise to get building permission that is if you are installing new stairs.
The normal relationship between the dimensions of the rise and going is detailed in Approved Document K, which states that twice the rise plus the going (2R+G) should be between 550mm and 700mm.
Your stairs are going to come in under that

As for the technicalities there is no reason why you can't make a very wide stringer by gluing two pieces together.