# Multiple non linear equations with shared parameters in brms

I am trying to perform a multivariate analysis with three responses variables where each response variable has its own formula. But the three formulas shared parameters. I want to perform a Bayesian inference that results in one posterior distribution for each parameter. However, using brms I am obtaining one posterior distribution for each parameter for each response variable. How can I perform the bayesian inference obtaining just one posterior distribution?

I tried with:

for_tot<-bf(Vo~((VmaxGK4K6GTP^2)+(VmaxdGK2K4GTPdGTP))/((K1K2K4K6)+(K2K4K6GTP)+(K4K6GTP^2)+(K2K4K5dGTP)+(K2K5dGTP^2)+(K2K4GTPdGTP)),
VmaxG+VmaxdG+K1+K2+K4+K5+K6~1,
nl=TRUE)
for_cyc<-bf(Vo_cyc~((VmaxG
K4K6GTP^2))/((K1K2K4K6)+(K2K4K6GTP)+(K4K6GTP^2)+(K2K4K5dGTP)+(K2K5dGTP^2)+(K2K4GTPdGTP)),
VmaxG+K1+K2+K4+K5+K6~1,
nl=TRUE)
for_lin<-bf(Vo_lin~((VmaxdGK2K4GTPdGTP))/((K1K2K4K6)+(K2K4K6GTP)+(K4K6GTP^2)+(K2K4K5dGTP)+(K2K5dGTP^2)+(K2K4GTPdGTP)),
VmaxdG+K1+K2+K4+K5+K6~1,
nl=TRUE)
form_two<-mvbf(for_cyc,for_lin,for_tot)

But this results in three distributions by parameters.