You mentioned that Project Performance has multiple dimensions. It means "Project Performance" variable is categorical? Or numerical and ordinal?  Or just dichotomous as project performance is good (coded e.g., as 1) or bad (coded as 0)?

The answer (optimal method) depends on character of  the dependent variable "Project Performance"  and also independent variables.

Assuming that all these inputs are numerical (or coded as numerical and this coding is really logically ordinal) you should perform

a) univariate analysis with each of 9 independent variables separately

and

b) multivariate stepwise selection  analysis where an optimal subset of 9 predictors will be selected by the model 

But detailed answer depends on the character of your variables.

As you have explained the case in detail a MLR seems more appropriate option, as it will give you the impact of all IV separately but in the presence of other IV. As the total number of variables are ten so you must try to have at least 10 responses for each variable, A larger sample will definitely help generalize your findings...

Regards

Rakhshan