Try a professional quality EQ unit and liberally experiment with
relatively small boosts in the midrange frequencies and/or cuts in the upper
midrange.
This is a good idea, however, one of the ways that designers achieve a "BBC dip" and yet still present a fairly flat on axis response is to lower the off axis response in the upper mid range. This drops the overall upper mid range energy. An EQ will not fix this aspect only a different speaker with wider dispersion will help.
A good way to tell if your speaker is evenly loading the room is to step outside and listen from some distance down the hallway - away from any direct sound. If it sounds totally convincing that there are people with instruments playing in your stereo room then you know the speaker is exciting an even sound field. If it obviously sounds like reproduced "Hi-Fi" then you know it is not evenly loading the room. It is surprising but the ear/brain can recognize this quite easily. The balance of the sound field tells you whether a piano could really be in the next room or not. An unconvincing sound field with a "distant" or far back presentation lets you know that the piano is somewhere else further away and therefore could not be in the next room.