Assign multiindex later to data variable


Following the tip of @jessegrabowski I add a pd.MultiIndex to my fit as follows:

fit.posterior.coords.update({'multiidx': train_data.index})

Next, I want to assign multiidx as coords to one of my data variables, p.
At the moment p has the following coordinates:

(chain, draw, p_dim_0)

How do I replace p_dim_0 with multiidx?
How do I remove chain and draw and only use multiindex/