As far as I know, there are currently two main types of predictive models available in PAD:
scoring (binary output)
spectrum (prediction of continuous behavior)
However, would it be possible to create one single model for dependent variable having multiple classes, i.e.: predicting propensities of purchase for multiple products, or multiple models would need to be built for each product in order to get individual score for single products?
You are completely correct, as PAD is for binary scoring it can only cover a binary outcome and as a scoring model it produces a probability for being positive. For multiclass scoring in PAD you would create one model per product (product x versus the rest).
As an aside for product and propensity modeling typically online learning, ie 'Adaptive Decisioning' is being used. It will learn on the fly for every outcome being captured, and creates one model per proposition. When the system encounters any new propositions it will create a new model on the fly, and models are constantly learning.
Earlier in the trail extended scoring models were being mentioned, but these do not relate to multiclass classification. An extended scoring model is a very special model that you use if for a non select part of your population you dont have the outcome. The prototypical use case is credit scoring, where you dont have behavior (default y/n for customers that were declined or that declined your offer). This is also called reject inference or outcome inferencing.