Conversation so far:
what is the multivariate research?
Rather than pursue a "univariate" research approach to psychology, studying the effect that a single variable (such as "dominance") might have on another variable (such as "decision-making").
what else can you tell me about it?
Cattell pioneered the use of multivariate experimental psychology (the analysis of several variables simultaneously).
what was being used before the multivariate?
He believed that behavioral dimensions were too complex and interactive to fully understand variables in isolation.
how did  the multivariate help?
The classical univariate approach required bringing the individual into an artificial laboratory situation and measuring the effect of one particular variable on another.
on another what?
also known as the "bivariate" approach.

Question: how is the mutlivariate research different?
Self-contained rewrite: how is the mutlivariate research different from the univariate?