I am not familiar with mcmcrun. But there are many metabolic models with more than 38 variables and 25 parameters. However, depending on the data you have at hand, it might be difficult to estimate all parameters. My advice would be:

1) try to decrease the dimensionality of the model (can you lump several reactions in one?)

2) try to find values for many parameters in literature and public databases (e.g. BRENDA or SABIO-RK)

3) study the correlation between parameter values, using parameter estimation methods

4) study the sensitivity of the model results to parameter values.

At the end, it might be that you only need to estimate precisely a handful of parameters.

I'm not familiar neither with mcmcrun. But here some potential additions to the response of Nicolas Gambardella

- depending on the number of the experimental data available and how they cover the overall behavior that you expect to describe with your model, you might be able to identify with precision only part of your model. In this context, you can check the structural identifiability of your model and asses the information content of your data

- it exist techniques to decouple the identification depending of the type of parameter (kinetic or stoichiometric)

- in non-linear model estimation problem, the most difficult part is often related to the definition of initial estimates. As mentioned above, the use of parameters estimates from literature is often useful as method for parameter estimation using constraint research space (i.e. the potential values for each parameters are constrained in a specific space). If no data is available in literature, multiple random shooting over the solution space should be performed to ensure a minimum the convergence of your solution

Is there a specific reason to use mcmcrun and not another one (e.g. simplex)?