**3. The Critical Review Combined with Text Mining**

When critically reviewing the methodological articles on multifunctionality, it emerged that these articles present two main "debates" regarding ISO-compliance practices. These two debates concern the application of system expansion (explained in Section 3.1 and related sub-Sections) and the identification of relevant partitioning criteria (see Section 3.2). In particular, Pelletier et al. (2015) identified three "schools" distinguished by the way they interpret the ISO hierarchy with respect to these three aspects: (1) the consequential LCA (CLCA) thinking school interprets system expansion as substitution, (2) the natural-science attributional school applies system expansion as enlargement and prioritizes allocation based on a physical parameter, and (3) the socio-economic attributional school applies system expansion as enlargement but prefers economic allocation. According to Pelletier et al. [9], these three schools are "internally consistent" but "mutually exclusive".

#### *3.1. Debate on the Interpretation of ISO's System Expansion*

The system expansion debate focuses on how and when the substitution method should be applied. ISO 14044:2006 recommends system expansion as a way to avoid allocation, but no further specification is provided regarding the differences between enlargement and substitution (see Appendix A for detailed definitions), and about its implementation in attributional or consequential LCAs. Substitution is often used as a system expansion approach in attributional LCAs (ALCAs), which is not perceived as correct by many LCA experts [5,9,35–38]. According to these practitioners, ALCA modeling should not rely on perturbation logic or counterfactual notions, such as substitution or avoidance of other products/processes (as also highlighted, e.g., by Majeau-Bettez et al. [35]). It is argued that the sum of the impacts accounted by attributional LCAs should add up to the worldwide impacts, and this would not be valid anymore if substitution were applied [5,39]. For this reason, Chen et al. (2010) concluded that the "allocation methods, even if perfectible, are still preferable to the system expansion method" (used as synonymous of substitution), because "system expansion does not ensure a global coherency between various LCA studies" [40]. On this basis, the use of substitution as a system expansion method in ALCA is not supported by any of the schools of interpretation identified by Pelletier et al. [9]. Similarly, Bailis and Kavlak, after applying substitution for the by-products of a biofuel, concluded that "the large disparity between system expansion and other methods raises questions about the validity of system expansion" [41]. Concerning system expansion by enlargement, this cannot be applied when the goal of the study requires the impacts of just one of the co-products or by-products to be obtained. In these cases, allocation cannot be avoided. For example, "In a milk production system that also produces beef, system expansion without substituting would lead to a system with a function of delivering both milk and beef" [42].

Other authors argue that ISO 14044:2006 does not acknowledge substitution as a system expansion approach. The reason is that ISO refers only to the addition of functions (i.e., enlargement) and not to the substitution of functions [3,5,43–45]. On these bases, several authors argue that a distinction of ALCA/CLCA should be present in future ISO 14044 [9,46] since, for them, this distinction is crucial to select the appropriate system expansion method (enlargement or substitution) (as also pointed out by [47,48]). By contrast, other authors argue the opposite, i.e., that substitution is generally recognized as a valid method for avoiding allocation within attributional LCA [49,50]. For many practitioners, substitution is considered as synonymous with system expansion [51,52]. Under this argument and considering the ISO hierarchy, substitution should be preferred to any allocation method [53–57]. Pelletier et al. [9] suggested that the equivalence substitution-system expansion might have originated

in a 1994 study authored by Tillman et al. [58]. The reason was that Tillman et al. [58] is a frequent citation when justifying the equivalence of substitution with system expansion. However, their study was published prior to the publication of the ISO standards.
