Making out of sample predictions using statsmodels SARIMAX with exogenous variable

Question

I would like to make out of sample predictions on the validation set on a fitted SARIMAX model from statsmodels in the following way:

1. Make predictions on the first 40ish steps of the validation set given the relevant exog and endog inputs without updating the parameters
2. Refit the parameters with only the first 24ish steps of the previous 40ish steps
3. Repeat step 1 with the next 40 steps after the 24 steps from step 2, so there will be some overlap in the predictions in consecutive iterations

What's the API-centric way of doing this? From the cross validation section on Forecasting in statsmodels, what I want to do is similar to what's supported by append and extend, but both seem to update the data on every call which is not desirable for step 1.