Funnelling (Fun) is a method for cross-lingual text classification (CLC) based on a two-tier ensemble for heterogeneous transfer learning. In Fun, 1st-tier classifiers, each working on a different, language-dependent feature space, return a vector of calibrated posterior probabilities (with one dimension for each class) for each document, and the final classification decision is taken by a meta-classifier that uses this vector as its input. The metaclassifier can thus exploit class-class correlations, and this (among other things) gives Fun an edge over CLC systems where these correlations cannot be leveraged. We here describe Generalized Funnelling (gFun), a learning ensemble where the metaclassifier receives as input the above vector of calibrated posterior probabilities, concatenated with document embeddings (aligned across languages) that embody other types of correlations, such as word-class correlations (as encoded by Word-Class Embeddings) and word-word correlations (as encoded by Multilingual Unsupervised or Supervised Embeddings). We show that gFun improves on Fun by describing experiments on two large, standard multilingual datasets for multi-label text classification.