What should be the output of the pdf for multivariate normal distrubition?
The PDF $p$ of a, say, bivariate Normal distribution with mean $\mu$ and covariance $S$ is a function that takes two parameters and has a scalar-valued output:

$$ p: \mathbb{R}^2 \mapsto \mathbb{R}$$

and is given by

$$p(x_1,x_2) = \frac{1}{2\pi |S|}\exp\left(-\frac{1}{2}(\vec{x}-\vec{\mu})^TS^{-1}(\vec{x}-\vec{\mu})\right)$$

where $\vec{\mu}\in\mathbb{R}^2$ is the mean of the distribution and $S\in\mathbb{R}^{2\times 2}$ is its covariance matrix. $\vec{x}=[x_1, x_2]^T$ is the function input and $p(x_1, x_2)$ is the function output.

So, the output is a scalar (a single value). Furthermore, the PDF can become larger than one for some input $\vec{x}$.