It's more common to find an aeronautical engineer with a CPL becoming a TP - the reason being that test flying is far more an extension of engineering work than it is of commercial flying.
The odds are that the "big boys" (Airbus, Boeing and the like) won't be all that interested in you because they tend to employ almost exclusively TPS graduates. Smaller companies however are often looking for part-time test flying talent, which might be the way in. This tends to mean either companies developing or producing light aircraft, or companies developing equipment - avionics or engines for example.
My suggestion, and I freely admit it's a loose one, is to look for smaller companies where the combination of flying experience and an engineering education is something that they might be interested in tapping into on a part-time basis. But it's a shrinking industry and a degree of luck is probably necessary to get your foot in the door. Alternatively if you are in the UK look to the PFA and/or BMAA, or if in the USA look to the EAA and perhaps get initially involved in the test-flying of prototype and homebuilt aeroplanes.
G