I'm not sure what's in your stock kit, but the BMW kits suck. I heard the ones they supplied with the old oilhead boxers are pretty good, but my generation hexhead and newer basically give you an engine oil cap key and a screw driver.
I don't talk too much about the technical side of motorcycling because I think there are better wrenchers out there who have better advice to give. We never really sat down to plan what tools we needed for this trip. Our toolkit consists of stuff that we've collected throughout all our previous trips, so there's some duplication and we're probably missing some stuff too. But it's carried us for three and a half years on the road, so I'm fairly happy with it.
Our tools are divided into two cases, one in the back above the Rotopax gas can. It's a Rotopax toolbox that uses the same mounting bracket as the gas can. It's waterproof and lockable but I don't really like it. It takes up too much space and isn't located in a good place. In the future, I want to move these tools to a tooltube and mount it further ahead on the bike, perhaps above the bash plate behind the front wheel. This kit carries tools that we don't use too often.
- Socket set with the sockets most used for our two bikes, an 8, 10, 11, 12 and 13mm
- Screwdriver set with different heads, socket extension
- Adjustable wrench
- lot of fasteners: electrical tape, two-way tape, hockey tape, duct tape (I'm kind of a tape fetishist), shock cords, zipties
- hex head set, allen key set, torx wrenches
- air compressor and the most accurate tire gauge we could find (digital sometimes not the best)
- tire repair kit
- extra engine oil
- fuel siphon pump
- work gloves and lots of plastic over gloves that we steal from gas stations
- super glue and blue threadlocker loctite
- replacement parts for known parts that fail on our bike (fuel pump, electronic key ring sensor, etc)
I carry a secondary tool kit up front in my tankbag, these are all the tools that we use more often so they're easily reachable.
- Hexhead set
- torx set
- mini screwdriver set
- Leatherman multitool
- More tape (yay!)
- zip ties
- replacement headlights and tail lights
- needlenose pliers
- mini adjustable wrench
- headlamp
- owners manual
- shock cord and zipties
- pen knife
There's stuff that we never used. Because we have extra fuel cans with us, we've never needed to use the fuel siphon. There's stuff that we thought about carrying, but decided not to because of the space. I am on the fence about carrying a torque wrench long enough to remove our wheels. We don't change them often enough and we've just borrowed the tools whenever we're staying with other people. I still might pick up one in the future...
If we had spoke wheels, I'd definitely carry tire spoons and an inner tube patch kit and spare inner tubes. One piece of advice I would give is to research all the stuff that normally fails for your bike specifically and carry spares. That would have saved us so much time and effort the last three years. Now that we carry all the spares... nothing breaks, so if anything, it's a talisman for good luck.
Only carry the tools and bits that fit the screws on your bike. So don't carry the entire socket wrench set with you, just the size of the heads that you'll need.
Also, look for any bike-specific tools that you won't find at the local motorcycle store, oil filter wrenches, etc. The BMW bikes use a special spark plug remover, you can use a screwdriver but you're at more risk to damage the spark plug holder. So stock up on these specialty tools because you won't be able to find them at the Canadian Tire. Or Kazakhstan Tire or whatever.