My M3 (2011 E93) also started this same squeak under quick acceleration when shifting gears at high RPMs. The squeak started around 34K-35K miles just before hitting 4 years of use when my warranty would expire. But luckily my local BMW dealership (BMW of Ann Arbor) has been very good to my cars and always welcome a challenge (especially since I'm sure they get paid by BMW to perform warranty services). Although my experience with previous dealerships have been terrible (all brands...), I gotta give credit when it's deserved; and my service advisor (Dereck) along with the service staff of BMW of Ann Arbor went above and beyond to get my issue solved.
* Short version of solution:
They changed all the belts and tensioners in the engine and the noise went away. Bam! "Simple" like that.
* Long version of solution:
It took a little over than 3 weeks to solve this issue. Yes, my car was in the shop during all this time. I was provided a normal 2015 328i as a loaner in the meanwhile. Better than not having a car at all although my M3 is so much more fun to drive. No comparisons.
Shop foreman testdrove it and immediately acknowledged the noise. He tried a few things but noise didn't go away. After about a week with no luck, he opened a case with BMW about it.
BMW happens to have engineers (this is what my service advisor told me) that can be sent to the dealership to help identify oddball issues when the local staff can't figure it out. And this is what happened here.
Second week: engineer contacted foreman via phone and provided some directions to try fixing the issue over the phone. About another week of failed attempts. No dice... Engineer scheduled to stop by and work on the car with local staff on the following week.
Third week: engineer arrives and starts troubleshooting the car. This is what it was done while the engineer was in the shop before they actually found the culprit (trying to remember what was written on the final paperwork I got):
1) installed "chassis ear" on the car to try narrow down the issue.
2) entire mechanical rear end was pulled off for inspection: rear differential, exhaust, shaft, etc... No fault was found. They assembled everything back with proper torque and specs.
3) chassis ear finally caught something coming from the engine area. Inspected the engine area for faulty components.
4) it was established the belts and tensioners, although not in bad shape, were not as prestine as they could. They then decided to change all of them and apply the proper tension as needed. Voila, problem fixed!
5) Engineer said goodbye and all was covered by warranty. I paid nothing for it, thanks God for that.
