The first question to ask is "what do you want the space for?"
You may find that basement will not provide for your needs at all.
One strategy with corner sites is to review what others with similar have built over the years.
Most will be unimaginative solutions but some may be unusual and worthy of your time.
If you build a basement you will tend to run into the perennial problems of groundwater, damp, subsidence, services, risk of flooding and a poor quality of space.
You need a very bold and imaginative solution to develop a basement space well.
Perhaps you should consider building forward of the existing building line, adding a double height bay window coming out a metre or more will add significantly to the amenity if the existing house on two levels and will probably cost less than a basement.
FWIW
ONQ.