There's always a balance between model complexity and interpretability. Of course, it'll be great if we can perfectly capture the comovement of all the bonds in the deliverable basket, but that would require the volatilities of all the bond's yields and the correlations amongst all these bonds as well -- it's not easy to come up with reliable assumptions for these...
Two-factor models typically depend on PCA to capture the co-movements of bond yields. My personal experience is that this works well enough -- in most environments, the first two principle components would capture 85-99% of the variances already. As to the residual, instead of thinking about "changes in curvature," I'd rather focus on the relative richening/cheapening of individual bonds, either relative to a fitted bond curve or on asset swap basis. This can be easily incorporated into your model.
At the end of the day, these models are meant to help with trading decisions, and 2-factor models are very easy to "think through." Personally, when looking at basis, I'd either take the duration/curve risks or hedge them out. This can be done very easily within a 2-factor framework.
Finally, there are so many intricacies involved when modeling bond futures/basis:
- Are you using the correct implied volatility?
- How do you model bonds that haven't even been auctioned yet? How rich should these issues be trading relative to current on-the-runs?
- Will the CTD and near-CTDs trade special in the repo market?
- Is the fed active and thus will repo rates increase/decrease substantially?
All of these factors can easily dominate the 3rd or 4th PCA factors...
P.S. I'm assuming you're not using one of those 2-factor short-rate models, right? Those don't work very well..