Composit component as container?

Composit component as a container (for other components - not part of)? Is it possible?
I assume - not :slightly_frowning_face:

Not sure I understand.
Isn’t it the role of the container component already?

Yes. But my intention is to build “middleware” container/component with additional functions. I need some features multiple times - not once - but differently on different page. Floating toolbar will be nice example.