Bayesian multilevel models provide an effective framework to borrow information between different data sources through the sharing of common features. In a nonparametric setting, a classic example is the hierarchical Dirichlet process, whose generative model can be described through a set of latent variables, commonly referred to as tables in the popular restaurant franchise metaphor. The latent tables greatly simplify the expression of the posterior and allow for the implementation of a Gibbs sampling algorithm to approximately draw samples from it. However, managing their assignments can become computationally expensive, especially as the size of the dataset and of the number of levels increase. In this talk, we identify a prior for the concentration parameter of the hierarchical Dirichlet process that (i) induces a quasi-conjugate posterior distribution, and (ii) removes the need of tables, bringing to more interpretable expressions for the posterior, with both a scalable and an exact algorithm to sample from it. This construction extends beyond the Dirichlet process, leading to a new framework for defining normalized hierarchical random measures and a new class of algorithms to sample from their posteriors. This is joint work with Claudio Del Sole (Bicocca University).