There are what we call GLM's with link functions. You can also use additive models which transform your input random variables (which sounds like something you should check out).
The thing though is that you need to describe what you are modelling: what are the variable types of your response and predictor variables? This answer will make a big difference on what you will choose with regards to analytic techniques as well as whether the assumptions are valid for those techniques.
With normal multiple linear regression, you can transform variables using various transformations (as is commonly done), but ultimately you need to say what you will be doing with the results and how you will use the model.