I have quite a bit of experience with clients with MS. Usually one side is impacted more than the other, and because of a series of falls, there are usually significant imbalances in addition to the neurological problems caused by MS.
I found that the first step is to strengthen all muscles as much as possible. Some areas may not immediately respond but with patient you may be able to build greater strength and thus a certain degree of confidence.
A client with severe balance issues will only improve existing compensations if you try balance exercises first. With one of my clients, I did strength (which is a very relative term with MS) for quite a while before even asking her to balance on anything. Eventually, I saw great improvements which were also in terms of confidence in the functioning of her body.
I would start very gently and rather ask too little than too much. Every exercise session should produce a feeling of “Wow, look what I CAN do!”
I wrote this on the assumption that you have medical clearance to work with your client. You client may also have seen a physical therapist who you should try to contact.
I wish you and your client all the best.