You can do some parameter tuning on the higher model to be applied to all the binary models generated. For instance, try different depths for the trees, different booster maybe… it would depend a lot on the context and data you’re using. The following resource may be helpful for XGBoost parameter tunings.

https://www.analyticsvidhya.com/blog/2016/03/complete-guide-parameter-tuning-xgboost-with-codes-python/