CMP with two recursive Heckman selection models and correlated error terms

My target model uses two Heckman selection models to model four equations (2 x binary selection variables: Y1 and Y2; 2 x continuous outcome variables: Y3 and Y4). I want to model Y3 conditional on Y1 (Heckman model 1) and Y4 conditonal on Y2 (Heckman model 2). The model has a recursive structure, such that Y3 affects both Y2 and Y4 (selection and outcome equations in the second Heckman model). Each dependent variable has a unique set of precitor variables (X1, X2, X3, X4). In the end, I want to correlate the error terms of all four equations.

Here is a depiction (please not that we model Y3 conditonal on Y1 and Y4 conditional on Y2, but the binary dependent variable Y1/Y2 is not a predictor of Y3/Y4):

Array

Recently, I came across the cmp package and documentation provided by David Roodman and I hope that I can use the package to implement this model.

Drawing from the documentation, the code for Heckman model 1 would be:

cmp (Y3 = X3) (Y1 = X1),
indicators(Y1 $cmp probit) nolrtest quietly

And the code for Heckman model 2 would be:

cmp (Y4 = X4 + Y3) (Y2 = X3 + Y3),
indicators(Y2 $cmp probit) nolrtest quietly

Is there any chance to combine these two Heckman models and correlate the error terms using cmp?

I'm looking forward to all ideas, many thanks in advcance.