I don't actually think 'triad of impairments' is a helpful term to use unless you are specifically talking about the diagnostic criteria for ASD. Yes, there is a triad of impairments, but those won't necessarily be evenly matched and will present differently in every child.
P levels and Pivats are not objective. They are the subjective judgement of a teacher who compares the child's current performance against a set of descriptors. If the child meets the descriptors for the P level, they then are deemed to be 'achieving P6', for example.
Depending on the child, their areas of difficulty, etc., you may expect to see quite good progress in some areas and less progress in others. That doesn't mean that the SEN provision is failing the child in those areas with less progress, necessarily, it may mean that they are simply less able in those areas. After all, we don't expect children who are NT to get the same grade in every subject at GCSE level.
DD1, for example, is 7.4. She is 'doing well' in maths. For her, that means that she has managed to count 60 coats at school. She knows the names of 2d shapes and some 3d shapes. She can use words such as heavier and lighter.
She is doing less 'well' in literacy. She is finding phonics hard to grasp, and is learning words using whole word recognition. She tries, but literacy is not going to be her 'thing' as much as maths.
7:49 of the SEN Code of Practice says:
"In the light of evidence about the child?s learning difficulty, LEAs should consider the action taken and, in particular, should ask whether:
the school or setting has, in consultation with outside specialists, formulated, monitored and regularly evaluated IEPs and whether the child?s progress, measured by criterion referenced or standardised tests, continues to be significantly and consistently less than that which may be expected for the majority of children following such programmes. "
That means that when you are making your argument for SA, you have to argue not that your DS is making less progress than same aged peers, but that he is making significantly and consistently less than other children who have the same provision as him.
"Although needs and requirements can usefully be organised into areas, individual pupils may well have needs which span two or more areas. For example, a pupil with general learning difficulties may also have behavioural difficulties or a sensory impairment. Where needs are complex in this sense it is important to carry out a detailed assessment of
individual pupils and their situations. However, the accumulation of low-level difficulties may not in itself equate with a school being unable to meet the child?s needs through school-based provision. In some cases pupils will have needs that are not only complex but also severe.
7:54 In considering evidence as to whether or not it is necessary to carry out a statutory assessment LEAs should bear in mind the particular requirements of the individual child, and whether these requirements can be met from the resources already available to mainstream maintained schools and settings in their area in the context of school-based intervention, monitoring and review arrangements"
These paragraphs clearly make the distinction between accepting that a child has SEN, even multiple SEN, and concluding that a school can't meet those needs from within its own resources.
It isn't necessarily so that the school are doing everything they can for your child. It's possible that they have further measures they can use without SA/Statementing, but aren't. If that's the case, that is what needs to change.
Statements are for children whose needs cannot be met by the school from within its own resources. So that's where the focus needs to lie. It isn't enough to show that progress isn't adequate. There is another step which is to show that the school cannot meet those SEN without the provision from the LA.