Use of unapproved ammo can be another perilous issue. Some departments now even go to the lengths of purchasing signature barrels to identify which weapon launched this particular projectile. The intensity of the aftermath of an officer-involved shooting is never fully appreciated until you arrive in court. Your police armorer has made recommendations for your duty ammo to match the needs of the department.
Now if you've read some gun writers, you may feel that you should make some selection of a toxic-tipped, nuclear-fueled, zombie-killing bullet of death. You would be making a serious mistake. Have you ever wondered why ammo is also inspected with your weapon inspections? Compliance!
If you did deploy this, you would be operating outside of the rules and regs of the department, which opens you up to all sorts of civil liabilities. Several cases of undocumented ammo have clouded post-shooting investigations, so stick to what you've been issued.
Carrying unapproved firearms is another huge mistake. The reason you were issued a particular weapon was not by happenchance. There are logical reasons. I've heard of several cases where after leaving the station the officer switched from the issued weapon to a fire-breathing larger caliber. All was good until its deployment.
I've heard the "tried by 12 verses carried by six" motif. However, if you are that uncomfortable with your issued weapon, try training a little harder. Bullet placement is paramount. Having a bigger caliber of ammo will not result in neutralization with a miss or poor bullet placement. Train and know your issued and secondary weapon systems.