I forgot to consider the targeting of the market. Should they target generic market or niche market?
As an idol, the most typical route is generic, because you want to sell as many as possible to as many people as possible. So typically management will choose the line of music that is easy listening and rather light and refreshing in the tone. Something that people will be encouraged to buy.
But their sounds might not really fit into this type.
I can't really see wide variety of age groups to be interested in their songs. Maybe that's why their customer base remains rather stagnant. They need songs that will be attractive to wider age groups and maybe wider gender groups, not only focusing on female population. However, once they deliver it, they need to maintain consistency of it and this is often the harder part.
To achieve this, I think they need to shift focus from fast tempo songs for a bit and try putting their hand into songs with few accompanying instruments so that their voice can be the focus of the attention. This is how they can show to wider public that they are really quite different than what many people think: they are even better in depth than the image they portrayed in the past.
But I also cannot ignore that they have been quite accumulating quite a lot of experiences in singing fast tempo songs. If they want to continue along the path, they may need to consider songs that people can sing along to and even better if people can also dance along to, as suggested by Papaya-san.
The major theme of the songs should largely remain the same: songs on situations concerning the rocking of the status quo, either intended on unintended.
However, for their international strategy, they might consider to go for the niche strategy instead. Rather than pushing for full English songs and trying hard to learn English, they should just place themselves and their songs as they are. Why do they have to be obliged to published songs in English to break to international market? Of course sometimes understanding the lyrics or the meaning of the songs is important, but doesn't they always say that music surpasses the language barriers? Why should an artist using certain language be placed above another artist that use different language? That's just arrogance.
But the most important above all is that they need to provide value to the listeners of their songs and people that support them as an artist and an idol. There should be something that they can serve to the world that is valuable to the world.
I might need to learn more on the value of music and artist to people's life, but by definition, the ultimate value of the entertainment world is of course to entertain. But why do people need to be entertained? Because when they are tired they want to just relax and let themselves be rejuvenated by the environment and atmosphere that the entertainment provides maybe. To distance themselves a bit from the daily reality of their life and just enjoy what the other people, in this case the entertainers, offer to them. It's as simple as that. So whatever these past decades' portrayal of any entertainers to be bigger and more important than any general public is just a load of Illusions, they are it turns out essentially are just a part of public servants.