Is there any other probability distribution model than gaussian for multivariate data
There are quite a number of multivariate distributions, in theory. At the outset, we categorize them as multivariate discrete distributions and multivariate continuous distributions. 

To start with, you may explore the following link for :
multivariate discrete distributions and the following for multivariate continuous distributions.

There are entire volumes printed on the subject, for example, books by:  N. Balakrishnan, Norman L Johnson, and Samuel Kotz and these books are published by John Wiley and Sons, Inc.