If it's the neighbour's wall then the Party Wall Act won't cover it anyway.
So you're planning on building a two-storey high wall wholly on your land, with foundations no deeper than that of [either your neighbour's or the Party Wall] the existing separating wall to support an rsj just to avoid serving Party Wall Notice and possible Award?
There is always scope for misinterpretation.
If my posts can be interpreted in two ways, one that makes you feel angry and one that doesn't, I meant the latter.
Everyday is an opportunity to learn something new.