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I don't know of any way to have more than two mark types in a single pane. Tableau uses a dual axis to get the two mark types, there's no triple-, etc. axis to get additional mark types.
The only place where Tableau will draw a dashed or dotted line is for trend lines and reference lines. Here's an older thread with some workarounds: http://community.tableau.com/thread/108247?start=0&tstart=0
Thank you very much for the reply Jonathan. Looks like this is one of the serious limitations we have in Tableau
Here is an example that I made long ago in version 5, before multiple mark types was a feature of Tableau.
Your limitation is your data source structure and contents.
As for a dotted line mark type in Tableau, that is a purposeful choice based on Tableau's intentions.
I knew as soon as I saw your post I was going to learn something new and I did. Thanks, Joe!
Very clever Joe.