Multivariate Binomial Variable

I’m trying to build a model for a situation where I have a vector of binomial trials, all of which are correlated. Stan has a useful tutorial for the special case where the trials are all Bernoulli trials and I want to use the probit link; however, I have a case where the trials are binomial rather than Bernoulli, and I’d like to use a logit link. Is there a way to accomplish this in either Turing or Soss?