I am often asked if a straw bale house can be built over a basement. The answer is always yes. A raised floor system, either over a basement or crawlspace, is no different than building a second floor on a bale home. Interior footings will likely be necessary to carry the load of the floor system. In some cases, you may need to step these down into a lower sectional basement for continued support. Once they are poured and in place, you can build your stem walls. You can use poured concrete or block, depending on your desired finish result.
With your stem walls in place, simply add your floor system to the top of the wall. Be sure to account for the dead weight of the bale walls when calculating your floor joist size and spacing and when considering how many interior beams or girders will be required to split the load across the span of the house. In some cases, you may need to build a secondary bearing wall directly below the interior face of the bale walls to transfer that load off of the joists. When necessary, this actually creates a great place for running plumbing and electrical in a finished basement.