Hey MurkleMan,
Yes you can do both; it's actually becoming rather common nowadays to combine hypertrophy training and strength training together. Doing both together will make it "harder" to achieve whatever specific goals you have BUT, given enough time, you can still reach those goals.
Your body's going to do what it does best and ADAPT. You do need to watch out for overtraining, both the muscles and your nervous system. You'll want to try and inverse the intensities (Heavy Strength Training + Light-Mod Hypertrophy) or (Light Strength Training + Full on Hypertrophy) so your body doesn't become to exhausted.
Just be mindful of your programming fluctuate the intensities based on your current goals.