This paper investigates how welfare losses for facing risks change as a function of the number of risk exposures. To that aim, we define the risk apportionment of order n (RA-n) utility premium as a measure of pain associated with facing the passage from one risk to a riskier one. Changes in risks are expressed through the specific concept of stochastic dominance of order n defined by Ekern (1980). Three configurations of risk exposures are considered. The paper first shows how the RA-n utility premium is modified when individuals wealth becomes riskier. This makes it possible to generalise earlier results on the topic. Second, the paper provides necessary and sufficient conditions on individual preferences for superadditivity and subadditivity of the RA-n utility premium. Third, the paper investigates welfare changes of merging increases in risks.