Extreme weather under two simultaneous index extremes
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The indices are not so independent of each other that extremes of different indices may occur on the same day. Days with each possible pair of different index extremes (such as extreme high NAM and extreme low PNA) do occur over the record. A small amount of analysis was done here to try to separate for instance from all extreme high NAM days the extreme high NAM days also with say high CTI (during El Niño) and low CTI (during La Niña).

In practice this tends to just highlight the individual indices and their effects, particularly their relative influences on given locations. To learn more about work looking at interactions between these leading teleconnection patterns, see the work by Roberta Quadrelli (a simple web search on her name should take you right to this work).