Is your feature request related to a problem? Please describe.

There are cases where in Kibana you have a regular flyout and you want to open a push flyout from a CTA. I am expecting that the push flyout should move the regular flyout to the left in order both contents to be visible. Right now, this is not possible. The only thing that works is opening a regular flyout above the already existing one but this is not useful as in the majority of the cases we want the content from both flyouts to be visible

Use case
One of the things that got released in kibana 8.11 and is going to be added in various places in the short term is the in-app editing of Lens embeddables. elastic/kibana#166169 This allows the users to edit their Lens embeddables by opening a push flyout. There is no need to go to Lens which I feel makes sense in the majority of cases and is going to increase the ux a lot. One of the problems we have on integrating this to other apps is that sometimes an embeddable can live in a flyout (a regular one). Opening a push flyout from a regular flyout doesnt work

I know that there are already some discussions on allowing the regular flyout to have additional columns but I wonder if making the 2 types of flyouts work nicely together is a faster solution.