The process of buying more or the rest of your Shared Ownership home is referred to as staircasing.
Most Shared Ownership leases allow you to staircase up to 100%. There are some that are capped at 80%. This is normally in villages or rural areas, the 80% cap is to ensure there are Shared Ownership homes locally for future generations. You should ask when enquiring about a particular home.
You can read our Guide to Staircasing below or if you prefer you can download a copy here.