Classification technique to classify categories in two variables when dateset has larger number of numerical variables and few data points

I’m doing data analysis and need to build a classification model.

Data set has 72 data points and

1. 37 numerical variables
2. Two categorical variables

categorical variable 1 has two levels A and B
categorical variable 2 has 4 levels W, X, Y and Z

What I have tried so far?

I couldn’t figure out how to build a two-step classification model. I could only classify into one categorical variable at once.

1. Logistic regression model for categorical variable 2

Did a PCA on 80% of training data and used the first 5 PCs (explained about 95% of variation). Then tested on the remaining 20%. had an accuracy of about 75%. I did 5 fold cross-validation

2. tried K nearest neighbor, Support vector machines, neuralnet in r (due to small number of data kicked this method)

What I need advice about?

Classification model to classify a data point into categorical variable 1 (Level A or B) and categorical variable 2 (Level W, X, Y, and Z) using r software.

I need a model that would do the classification into both variables at once if possible. Any direction or guidance is appreciated.