When using lower probabilities to model uncertainty about the value assumed by a variable, 2-monotonicity is an interesting property to satisfy, as it greatly facilitates further treatments (such as the computation of lower/upper expectation bounds). In this paper, we show that multivariate joint models induced from marginal ones by strong independence, epistemic independence or epistemic irrelevance do not usually preserve such a property, even if it is satisfied by all marginal models. We then propose a joint model outer-approximating those induced by strong and epistemic independence and study some of its properties.