Two header templates

Is it possible to have two active header templates and display them simultaneously (conditions “Entire website”)?

I ask because I want to simultaneously have a pull-out menu (sticky) and another, graphic element that is static, standing in a fixed place on each page. Unfortunately, with one header template with sticky option I can’t do it, because the whole template is covered by “hiding”, along with this static element.

And two templates displayed simultaneously would solve this.
I tried, but unfortunately one appears, the one with the smaller id, but maybe I don’t know how to enable it.

I hope I understand you correctly.
Maybe consider adding both elements to one template. You can then display the template on all pages and add conditions to each.
Eg. You can include the element to be fixed in the template as well as the pulldown element. Consider that you don’t need to set the whole template to sticky and that you may only set a part of the template allowing you to integrate other elements such as your fixed element.
Just some food for thought and hope it helps give you a few options.