Panels content wrapper
You can definitely use the Panels Extra Styles module to wrap multiple panes in as many tags as you need.

On the first pane of your new group click the option cog and, under the Style section (which should read No style), choose 'Change'. Change the selected style to Wrapper:Raw and enter your opening tags in the text area 'Content prefix'. Leave the suffix area blank (as you don't want to close any tags yet)

Save the changes and then do the same with the last pane you want to group. This time close all the tags opened in the first pane by entering them in the 'Content suffix' text area.

Save and update your panel page and et voila! Your panes are grouped with your own HTML!