The induced ordered weighted average is an averaging aggregation operator that provides a parameterized family of aggregation operators between the minimum and the maximum. This paper presents some new generalizations by using Bonferroni means (BM) forming induced BM. The main advantage of this approach is the possibility of reordering the results according to complex ranking processes based on order-inducing variables. The work also presents some additional extensions by using the weighted ordered weighted average, immediate weights, and hybrid averages. Some further generalizations with generalized and quasi-arithmetic means are also developed to consider a wide range of particular cases including quadratic and geometric aggregations. The article also considers the applicability of the new approach in-group decision-making developing an application in sales forecasting.