Side by side view with a side-menu

Potentially, but it will require the use of some JavaScript for brute force the arrangement of the views. A similar approach is used to move a view that is used as a header to be above a tab control since K2 puts tabs at the top, so a more involved rearrangement should be possible.

Here is a blog post that covers moving a view above the tab control as a starting point.

So, the short answer, no, not with currently delivered designer tooling.

Possible with some JavaScript creativity.