*Appendix A.4. Type of System Expansion Approach and Substitution*

System expansion means the enlargement of the boundaries of the system under investigation to include additional processes and functions. As mentioned above, expansion of the boundaries can be used to avoid allocation. There are two possible approaches to avoid allocation by expanding the boundaries: enlargement (see Figure A1 for different types of enlargement) and substitution (see Figure A2). By considering the subtraction as "a negative addition" [51], substitution is considered by some LCA practitioners as a form of system expansion used to isolate the impact of just one function from a multifunctional process.

One can apply system enlargement by modifying the functional unit to include all co-functions (case a of Figure A1). This approach is not possible when the goal of the study requires to determine the impacts of only one of the products because the results at the level of one single product would not be available. System enlargement is also often used for comparative assessments. In case b of Figure A1, the aim is to compare process P1 (providing functions A and B) with process P2 (providing only function A). One needs to add to P2 another process for producing B in order to allow the comparison for the same outputs. Similarly, in case d of Figure A1, the aim is to compare a process producing A with a process producing B (for example, comparing the impacts of two products which could be made from the same raw material). In this case, one needs to add alternative processes for making both A and B in order to make a meaningful comparison. Even though these processes are not initially multifunctional, system enlargement is applied to allow for a fair comparison. One can also apply system enlargement in open-loop recycling systems. In the example of system enlargement from ISO/TR 14049, open-loop recycling is solved with a closed-loop procedure that includes the entire recycling processes into the same system boundaries (like case c of Figure A1).

**Figure A1.** Different ways to apply system expansion as enlargement-addition of functions. In black: multifunctional process before applying system expansion. In blue: process after the expansion of the boundaries/addition of functions. (**a**) Changing the FU to avoid allocation. (**b**) Adding extra processes (P3, delivering B) to a system (P2, delivering A) that is compared with another system (P1) delivering several functions (A and B). (**c**) Applying closed-loop recycling to a system (P) where one of the outputs (B) is used as a material input in the same product system (P2 represents the intermediate processing of B that allows its re-use). (**d**) Adding extra processes (P3 and P4) to compare systems that provide different functions and that at the beginning were not multifunctional.

**Figure A2.** System expansion by substitution (reduction of functions). The investigated system (P1) delivers two products (A and B). Alternatively, product B can be produced by another system (P2). The substitution method proposes that the impact of producing A (only) by process P1, corresponds to the difference of impact between P1 and P2.
