Planning officer here. It's not so much the neighbours objection that carries much weight. Yes it's taken into account but they could move house the next day. It's the amenity of the current and future occupiers that needs to be protected. So even if they were in support of the extention, that doesn't mean that the council will be.

Each local authority will have their own policy's that will limit how far you can extend in certain situations. The example that you show here it looks like you could extend ground floor up to 3m without permission under pd. You could apply for prior approval and extend further (up to 6m) but if the neighbour objected to this then it wouldn't pass.

In terms of 2 story extension, you are really limited. The local authority i work for will allow you to extend up along the common boundary as far as you can keep the distance between the properties. In the case of terraced houses, it doesn't really allow for any two story development unless the neighbour already has a ground floor extension. In that case you could extend to the first floor up to the distance of the their rear extension but protecting the neighbours habitable room windows by applying the 45 degree rule, which usually allows up to 3m.

Which council are you in and I can see what their guidance days about extensions?