DoE with nominal input variable

[#1]

We have three factors and one response variable.
Factor1 has 2 levels, Factor2 has 2 levels, and Factor3 has 3 levels. All factors are nominal variables, while the response variable is numeric. According to the experimental design, 12 experiments were conducted, covering all possible factor-level combinations .

I have already performed an SLS analysis, including two-factor combinations. Are there any additional statistical tests that could be applied? For example, is there a method that allows testing the combined effects of multiple factors? Any way to visualise these effects?

Thank you in advance!

[#2]

By nominal variables, do you mean categorical? Since your data was collected via DOE, you should already have a model in mind. It is much easier to comment if you attach your data table (anonymize it). It appears you ran a factorial with no replication. First analysis should be practical. Did the response variable vary enough for you to interested in assigning that variation? If so, then you should evaluate the data set for integrity (were there any unusual data points?). You can check this again once you have a simplified model and residuals are calculated, but it is worth having a look before quantitative analysis. For quantitative analysis there is no one right way. You might typically start with the fit model platform. Saturate the model. Use half normal plots for statistical significance and Pareto plots of effects from practical significance.  Simplify the model by removing uninteresting terms from the model (you can use Adj R-sq, delta between R-sq and Adj R-sq, RMSE to help). Run the analysis again and get residuals (many plots are available). You can now use the prediction profiler and interaction plots to view the data graphically.