A classic problem in the mathematics of juggling is to give a basic enumeration of the number of juggling patterns. This has been solved in the case when at most one ball is caught/thrown at a time, with the simplest proof being due to Ehrenborg and Readdy by the use of cards.

We introduce a new set of cards that can be used to count multiplex juggling patterns (when multiple balls can be caught/thrown at a time). This set of cards models the correct behavior and avoids the problems of ambiguity; on the other hand the cards are no longer independent. By use of the transfer matrix method combined with the cards we enumerate multiplex juggling patterns with exactly b balls and hand capacity κ, and include data for κ = 2, 3, and establish some combinatorial properties of the cards.