determiners of the same type with the conjunctions and and or: his and her children, two or three beans.

The same answer says that "I drove this my car" is wrong. The form "this" followed by a possessive is now rare, but was once more common, especially in formal writing. In particular sentences such as:

It is a mistake to regard aspects of this our present society as unchangeable rules.

were sufficiently common to be a style marker in the writings of the late Robert A Heinlein. 
Since the question title asks about using "two possessives in a row", this can certainly be proper. 

This was John's father's watch.
This was King Mark's wife's cousin's castle.

are both quite correct.

Rising oil prices and the finite nature of fossil fuels have led to an increased demand for alternative fuel sources. One feasible and renewable option is the conversion of biomass material into biofuel. Typically, the conversion process involves the flow of the biomass material through a series of chemical, thermal, and mechanical treatments. Currently, however, generating the flow of the biomass material through the series of treatments is difficult and expensive. Often, significant amounts of auxiliary materials and energy are required to generate the flow of the biomass material through the series of treatments. In order to maximize the efficiency of the conveyance of the biomass material through the series of treatments, and hence reduce the overall cost of generating the biomass flow, the proper design of the