2(ii). Point counterfactual identification with non-SCMs-based approaches. Alternative, non-SCM-based definitions of the counterfactuals exist, e.g., transport-based counterfactuals [32, 96], and conservative counterfactual effects [4]. Still, for the identifiability of ECOU [ECOT], they also rely on additional assumptions such as monotonicity. These approaches were shown to coincide with standard SCM-based counterfactuals when the latent noise can be deterministically defined with observed data. Therefore, they coincide with BGMs.
3(i). Discrete partial counterfactual identification. Partial counterfactual identification was rigorously studied only for discrete SCMs or discrete outcomes. For example, bounds under no assumptions were derived for counterfactual probabilities [6, 80, 82, 103, 127]. More general counterfactual queries can also be tackled with response functions framework [6] and, more generally, canonical partitioning [112] in combination with deep neural networks [97, 137, 141, 142, 143, 147]. The same idea was used for causal marginal problem [46, 115] where the authors combined different experimental and observational data with overlapping observed variables. However, response functions framework and canonical partitioning can not be extended to the continuous setting in practice, as their computational complexity grows exponentially with respect to the cardinality of the observed variables. Hence, the aforementioned methods are not relevant baselines in our setting.
3(ii). Continuous partial counterfactual identification of queries with informative bounds. Certain counterfactual queries have ignorance intervals with informative bounds, which have a closed-form solution using Frechet-Hoeffding bounds for copulas. For example, informative bounds were derived, e. g., for the variance of the treatment effects [2],  $\operatorname{Var}(Y_a - Y_{a'})$ ; for the CDF of the joint potential outcomes distribution [37],  $\mathbb{P}(Y_a, Y_{a'})$ , and other related queries [4]. Yet, these bounds cannot be applied to our setting, as our query of interest, namely, ECOU [ECOT], has non-informative bounds and, thus, requires a sensitivity model.
3(iii). Continuous partial interventional identification. The problem of partial interventional identification arises in semi-Markovian SCMs and usually aims at hidden confounding issues of treatment effect estimation [88]. For example, instrumental variable (IV) models always obtain informative bounds under the assumption of instrumental validity [48], so that partial identification is formulated as an optimization problem [55, 68, 99, 145]. In other cases, hidden confounding causes non-informative bounds and additional assumptions about its strength are needed, i.e., a sensitivity model. For example, the marginal sensitivity model (MSM) assumes the odds ratio between nominal and true propensity scores and derives informative bounds for average or conditional average treatment effects (ATE and CATE, respectively) [15, 35, 40, 41, 60, 61, 62, 89, 98, 126]. The outcome sensitivity models [15, 106] and confounding functions framework [17, 109] were also introduced for the sensitivity analysis of ATE and CATE. [49] develops a sensitivity model for ATE assuming a noise level of proxy variables. All the mentioned sensitivity models operate on conditional distributions and, therefore, do not extend to counterfactual partial identification, as the latter requires assumptions about the SCM. Some methods indeed restrict functional classes in SCMs to achieve informative bounds. For example, linear SCMs are assumed for partial identification of average treatment derivative [5]. By developing our CSM in our paper, we discuss what restrictions are required for SCMs to achieve informative bounds for partial counterfactual identification of continuous outcomes. Nevertheless, the methods for partial interventional identification are not aimed at counterfactual inference, and, thus, are not directly applicable in our setting.