Decomposing a probit/logit regression

In an econometric work, I want to assess the causal effect of n variables on a binary character variable y, while I highly suspect that the relation between one of these regressors, say x (which is numerical), and y, is dependent on the value of x. Thus, I aim at using a non-parametric (local) logistic regression.

In order to avoid the curse of dimensionality, and because a classical logistic regression seems appropriate for the relation between the n-1 other variables and y, it would really help me to get answers to the following question:

Is their a way to do a classical logistic regression involving the n-1 first regressors, then to do the non parametric regression involving simply x, and then to link those two regressions to have the causal effect of each variable ?

In a linear model, I would run the first regression between y and the n-1 regressors, then run a non-parametric regression of the residual on x, but I do not think it is possible to do it in a logistic framework.

Thanks a lot,

PB