Is there a model that can adapt to additional new training data with different columns?
A tree-based algorithm can do that.

The point is that you need to train the model with the union of the possible columns that can exist the different batches.

Moreover you need to account for missing values so that the model can learn to recognize a missing and handle them: you need to recode the missings with a proper value, for example you can create a new level for categorical variables and recode the numerical in the standard way (zero, mean, extreme value, etc.)