It really depends on DS’s presentation, what type of further education courses he wants to do, and whether he can cope with some off-site provision or if he needs all the curriculum delivered on site. The latter is because post 16 some SS have arrangements with other local schools/colleges.
You could also look at Breckenbrough, Boveridge College, Unsted Park and West Kirby.
Depending on how DS's needs present, More House may admit.
Depending on how DS’s MH conditions present, West Heath may be suitable, and if you are around Devon, it is worth looking at Magdalen Court School depending on DS’s MH needs.
If you happen to be within travelling distance of Worcestershire, you could look at Chestnut place, but it isn’t residential.
If you happen to be within travelling distance of Sheffield, you could look at Kenwood Academy, but it isn’t residential.
Not all these will be suitable, it depends on DS’s needs.
Some find Gretton and Cambian Wing overwhelming.
Cambian schools have a mixed reputation and some parents are put off by that.