Different people are going to react to codeine differently.
Adding to what Colleen said, taking higher amounts of Tylenol/Acetaminophen is very dangerous. If your Tylenol 3 pills are not relieving pain do not take more of them. I know a gentleman who was in the hospital for 6 months and nearly died after taking too much Tylenol.
If Tylenol 3s are not relieving your pain ask your doctor for a stronger medication rather than just taking more of them. Naturally you shouldn't take any medication in higher doses than recommend or prescribed but products containing Tylenol/Acetaminophen are particularly dangerous to overdose on.
In a sense, yes...you can be the kind of person who can take several of them without them having any obvious effect on you (I'm the same way - they're like eating candy), however, that doesn't mean that they don't have internal or long-term affects. Taking too many can still cause overdose and liver damage.
I figured that cus I take some for a headache and they do nothing and a few weeks ago I was given t3's for my wisdom tooth pain and hours later they still hadn't kicked in