I get a lot of questions about what height a bale building can be. People want to know if they can build three story homes with straw bales or if they are limited to one story. That all depends on the way you chose to build: load bearing or in-fill. There are differing opinions on how tall a load bearing structure can be however, and some newer applications are pushing the envelope to its limit. A safe assumption, especially if you plan to get code approval and do not have specific engineering to show otherwise, is that the load bearing structure will be limited in height as compared to a post and beam structure.
You can build tall structures (three stories, etc) with straw bales if that building is a post and beam structure or otherwise structurally framed with something other than bales. The bales would be used as in fill. The frame handles the load and the bales offer the insulation and “feel.” This is a great way to build more complex designs as well because there are more options available to you with the inclusion of a structural frame
If you want to build load bearing walls (no structural framing other than the bales themselves), you can only go single story, plus a loft, if designed properly. The height of the wall is limited to a height vs. wall thickness ratio. The thicker your bales, the taller you can go. After a three string bale, adding additional thickness to increase height becomes a waste of materials and space in 99.9% of the cases. Load bearing straw bale homes are more simple in design as a result and are often easier to build. As always, identifying what is most important to you before you start building is key. Make sure you are focusing on the most important aspects of the job during design, and you will end up with what you want in the end whether it be simple and load bearing or complex and structurally framed.