Sawtooth Software's default experimental design routine "Balanced Overlap" already does a very nice job of supporting all 2-way interaction effects, assuming you use enough versions (blocks) of the questionnaire...typically somewhere between 5 to 10 versions is enough. However, our software doesn't automatically support 3-way interaction effects (though there is a power user workaround).
With many versions of the questionnaire, especially dozens or more, you should have a reasonable design to estimate 3-way interaction effects, though you'll need to manually collapse two attributes into one attribute, or three attributes into one attribute (via manual data processing steps in the software). If collapsing two attributes into one attribute, then you need to submit a two-way interaction between your collapsed attribute and the third attribute.
But, to formally (and more precisely) support both the design and estimation of a 3-way interaction effect, you'll need to collapse your attributes ahead of time. For example, if you knew ahead of time which 3-way interactions you wanted to estimate with highest precision, you could take two of your 3-level attributes and make them a single 9-level attribute. Or, if you took a 3-level attribute and a 4-level attribute you could collapse them into a single 12-level attribute, etc. The Balanced Overlap designer achieves a very high degree of 2-way attribute level balance, so collapsing two of the attributes into one would be enough to secure excellent interaction effects between the collapsed attribute and a third one.