I planned to dig more into using simulations to observe how different methods work out in practice, but realized that generating logistic models is not trivial. Enter simstudy, an R library that can do exactly that. The author pointed to a recent 2023 article describing the procedure by Peter C. Austin named ’ The iterative bisection procedure: a useful tool for determining parameter values in data-generating processes in Monte Carlo simulations’. The article can be found online here.
What are you looking to solve? It sounds like there is a question behind your question.
The shape of an ROC curve is a characteristic of the model I think. Some models can for example perform better on lower probabilities, other models fair better on other parts of the scale, and then there are models that perform the same across the scale. Changing the shape of the curve means changing the characteristics of the model.
By the article AUCs are changed by shrinking model coefficients. I assume applying the same procedure to the same model equation ends up with the same curve, barring some sampling variation on the generated data needed to calculate a curve.