I have no personal experience of PIP but I do have benefits knowledge.
The decision should explain how they decided how many points to award but some are more detailed than others.
It would be worthwhile contacting DWP to ask for a copy of the assessment as it's not unknown for incorrect information to be noted in the report.
Have a look at what all was written, identify any inaccuracies and include this in the Mandatory Reconsideration (MR).
If the original decision is not changed, DWP has to explain why. You can then appeal to HM Courts &
Tribunals Service (HMCTS) who will then send a copy of your appeal to DWP. They will look again at the decision and change it if appropriate.
If they cannot change the decision, they will write an appeal submission to HMCTS and send a copy to you. An indepdndent tribunal then looks at the case again.
Anyway, go for it and good luck!