Skydive Interlaken runs out of helicopters with 5 slots, so if there's two tandems there's often a spare slot for a fun jumper. They fly to 8.5-10.5k above Interlaken, or out next to the Eiger (which I didn't get to do). The offices are about 30 min walk out of town, so pretty easy to get to.
I did 3 jumps over Interlaken in one day in March, which was when there was still some snow on the mountain tops, but wasn't too cold down in the valley. If you've only ever jumped out of planes in rural areas its quite the experience. Best appreciated head-up and watching the mountains go up while you fall down.
The staff were friendly and super-accommodating, going so far as to help me arrange jumping at Skydive Switzerland the following day.
Definitely worth a visit if you're out here!