Any band or act that has a break-out in terms of their Audience size is going to eventually transition from break out to "mature" status. A mature Artist/band has an existing Audience, a track record as measured by album sales and ticket sales in the top 50 markets in the US/UK/EU and a rate of momentum. Depending on how well an Artist is doing in these measurable areas they may or may not have a couple of common problems:
1. Slowing/negligible rate of Audience expansion.
2. Lack of motivation of existing fans.
There are a few different ways that Artists deal with these issues:
1. Stop existing project, start new project.
2. Attempt to "move up" in terms of label/management/etc.
3. take time off from existing project and do something else entirely or nothing at all.
I would argue that none of these approaches is optimal, and rather the proper thing to do is to start another project that works in conjunction with the existing project but focuses on recapturing a "break out" status rather then aping the activities of a mature Artist.
It's important to keep in mind the effect of time on the Audience for new music. Typically, Audience members are more likely to like new bands when they are young. Let's call them "college students." You can think of the Audience for a new Artist like the incoming class of a college- freshmen come in and seniors go out but every four years you have an entirely new group of potential Audience members.
So let's say an Artist is in band 1 that "breaks out" in 2009. They've got three or four years to establish themselves in the existing Audience, but then, by the time they reach mature Artist status there is an entirely new group of potential Audience members but guess what? They don't give a shit about mature Artists- they want new Artists. If you are an ex-Break Out the only way to reach the new Audience members is by creating a new Act that can achieve "break out" status.
For the purposes of the first act- the mature act- there is no downside, because the potential Audience for a new Artist is entirely different than the Audience for a mature Artist and the two hardly interact.
These efforts are commonly called "side-projects" and most of what can go wrong with an attempt along these lines is encapsulated by the secondary associations of the term "side project." Like, it's a part time job subservient to the mature Act or that it doesn't deserve to be taken seriously or that it somehow compromises the existing Audience for the mature Act.
That is all poppy cock- properly done any occupation should be "part time" because otherwise the worker will get exhausted- being in a potentially self-supporting band is exactly the same as being a doctor or lawyer in that regard. The Artist wants to be able to take time off BUT- and this key- wants to continue to keep existing Audience members for the mature Act motivated.
Audience motivation is a tricky subject not fully understood, but it basically interacts with the momentum of a specific Artist- a motivated Audience increases momentum, an unmotivated Audience decreases momentum.
I would argue that starting a new Act is the best way to potentially motivate an existing Audience for a mature Artist because it creates a new context for that Act and because the new act can attract new Audience members that have a potential to migrate to the more established acts- something that WOULDN'T happen in the context of a mature Act putting out new records and touring.
I think the key to success when it comes to diversifying Artistic identity lies in respecting the integrity of each Act. From the perspective of a mature Artist, it might seem ludicrous that a new Audience member would pick up on the new Act and remain entirely ignorant of the more established act but guess what? THAT IS HOW IT WORKS.