Internal changes will not affect CP, but will obviously change the CG and therefore the CG/CP relationship for stability.
-Ken

Ditto to what Ken said. You might have to add weight to the nose to compensate. If you know where the center of pressure of the design is and can balance the rocket to find the center of gravity, then with this information you can determine if your CG is ahead of the CP, and preferably, at least one caliber, or the CG is one tube diameter ahead of the CP. These dimensions are taken from the nose going backwards to the tail. If you do not know where the CP is, there are free rocket design programs on the internet, or you can get the trial version of RockSim and use it to determine where your CP is suppose to be, and go from there. I hope this helps.

Adding to Ken's and Bear's responses,,,, another way to think about CP - center of aerodynamic pressure - that is the pressure exerted on the external geometry of your rocket as it travels through the air. So the only way to change the CP is to change the external geometry - fin shape / size, airframe length etc...

A 'fun' exercise is to run one of your rockets through the Barrowman equations to calculate the CP (Appendix II in Stine's Handbook of Model Rocketry)... 'fun' if you're a demented sado-masochistic former algebra nazi... but it does drive home the factors that affect CP...

There is another way to find the approximate center of pressure of a rocket without going through the Barrowman equation. You make a two dimensional model of your rocket out of stiff cardboard. Another way to describe it is that you have a full size drawing of your rocket's profile. Glue it to a piece of cardboard that will not fold-up easily. Then cut out your drawing with the cardboard and find the balance point of your cardboard cut-out drawing. It will give you a rather close approximation of where your CP is on your rocket. Then you can build your rocket, and measure the actual location of your CG. As long as your physical CG location on your 3D model is at least one body tube diameter ahead of your CG/(CP) on your 2D model, you should be OK. And I hope that helps also.