Is the question can you take more than 3 bags, or can you take more than 3 bags for free?
If the latter, as Miles Ahead suggested, just pay the extra bag fee of whatever it is these days?
Mrs Limey isn't known to travel light and if i remember correctly would check 4 bags on trips to South America, in economy, with 3 free and 1 paid as a UA *G.
I don't think they changed the rules so that it is only possible to check 3 bags in total.. but there may be capacity constraints on some routes at some times such that extra baggage is not permitted, but I'm sure someone will correct me if I am wrong. :-)