As well as working with stacks made of tasks and subtasks, you can switch between stacks. You can suspend a task stack, and resume another. (Suspending your current stack happens automatically on resuming another; you do not need to do it manually.)
To start a new task stack, from scratch, suspend your old one manually with the command sidebrain-suspend-task and start the new one with the command sidebrain-begin-task.
There are two ways to select a suspended task and make it current:
See Working with projects for details of the sidebrain project system.
When you suspend a task, it is automatically stored in the project from which it came. (In fact, it always remains part of that project.)