DI2: Can I configure different gears for each bike profile ?

Every Di2 is unique as "sensor". The sensor is configured with it's chainring and cassette configuration. So yes, each Di2 bike has its own configuration, even extra channels are per sensor and per bike configurable. 

To be clear, an amplifying what Ivan has said...there are not bike profiles. Just sensors. Set up each sensor as you desire, and when it connects, then it's setting are being used.

Hi Garmin-Blake, many people would be very happy if Garmin adds the option to appoint a specific bike to a specific activity profile. 
i do not understand why this is not possible. There is clearly a strong wish…..

For the above issue you don't need bike profiles as each bike has its own Di2 system and the Di2 system sends across the gear information for the Edge to use if you enable the automatic setting on the Edge. You configure the gear sizes on each Di2 system using e-tube.

Even if you configure the gears manually that information is associated with each Di2 system.

How about if I have different wheels with different cassettes for the same DI2 bike ?

Any ideas how to manage it ?

You would need to either use e-tube to update the settings when you change wheels or change the gear sizes on the Edge.

That's what I thought....not practical though 

Thanks

No easy way around the situation at the moment.

It would be nice if maybe Shimano added a RFID chip to the cassette and a reader into the rear derailleur. Then the Di2 system could auto-update.

Being able to have different bike profiles, for the same bike probably would be easier and less costly (it was available before)