I have mentioned it before, but I once used 16C73 (I'm embarrassed to say that I ever used 16 - series chips). The 16C73 was one in a ceramic package and a quartz window (it was UV-erasable, remember those?). Because it had to be put into an eraser for 10 minutes every time I wanted to reprogram it, I was constantly plugging it into, and pulling it out of, a nylon 3M proto-board. After one such insertion, I smelled something and looked over at the proto-board. Smoke was rising! I shut off the power and (stupidly) used my finger to see just which component was overheating. I touched the PIC and got a blister on my finger. After the PIC had cooled down, I removed it from the protoboard, and the 'groove' under the chip was melted. The nylon was dark brown as well. I noticed that I had installed the PIC backwards.
I was sad that I had to throw the PIC away (the erasable ones cost $20 each back then), but before I did, I put it back in the protoboard in the correct orientation. It worked!!!

About the same time (also with a PIC16C73), I needed a 20Mhz crystal. I didn't have any, but I had lots of TTL 'can' oscillators. I didn't have any 20Mhz parts, but I did have a 24Mhz oscillator. I tried it. It worked - no problem. So I kept plugging in higher and higher frequency oscillators. It ran fine at 57.6Mhz, but didn't work at 64Mhz. I can't say that I tested everything at that frequency, but it did a fine job of reading the A/D and adjusting an EEPOT in a "tracking" mode.
VCC was 5V. Who knows what it would have done if I had raised the voltage to 11V!

So - you can overclock PICs.