Conversation so far:
What is multivariate research?
Raymond Cattell pioneered the use of multivariate experimental psychology (the analysis of several variables simultaneously).
What else can you tell me about multivariate research?
The multivariate approach allowed psychologists to study the whole and their unique combination of traits within a natural environmental context.
What approach was being used before the multivariate?
Univariate and bivariate research approaches were more commonly used before the multivariate approach.
How did the multivariate research approach help research?
Multivariate experimental research designs and multivariate statistical analyses allowed for the study of real-life situations that could not be manipulated in an artificial laboratory environment.

Question: On another what?
Self-contained rewrite: Rather than pursue a univariate research approach to psychology, studying the effect that a single variable might have on another what?