Early classification of time series assigns each time series to one of a set of pre-defined classes using as few measurements as possible while preserving a high accuracy. This implies solving online the trade-off between the earliness and the prediction accuracy. This has been formalized in previous work where a cost-based framework taking into account both the cost of misclassification and the cost of delaying the decision has been proposed. The best resulting method, called ECONOMY-γ, is unfortunately so far limited to binary classification problems. This paper presents a set of six new methods that extend the ECONOMY-γ method in order to solve multiclass classification problems. Extensive experiments on 33 datasets allowed us to compare the performance of the six proposed approaches to the state-ofthe-art one. The results show that: (i) all proposed methods perform significantly better than the state of the art one; (ii) the best way to extend ECONOMY-γ to multiclass problems is to use a confidence score, either the Gini index or the maximum probability.