We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with continuous latent variables that enter as inputs into a single metamodel that simultaneously learns the response surfaces of all of the systems. Bayesian inference is used to determine appropriate beliefs regarding the latent variables. We explain how the resulting probabilistic metamodel may be used for Bayesian optimization tasks and demonstrate its implementation on a variety of synthetic and realworld examples, comparing its performance under zero-, one-, and few-shot settings against traditional Bayesian optimization, which usually requires substantially more data from the system of interest. Some literature refer to these as "qualitative" features, though this seems somewhat of a misnomer since certain types of attributes in question can be numerical in nature, such as zip codes, yet are clearly unsuitable to treat as numbers in a model; others may not be quantitative, but are nonetheless precise (e.g. the name of an operator), yet "qualitative" does not convey this preciseness.

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