When you switch to the federal mobility budget, the law does not allow you to receive a mileage allowance in addition.
However, you can have the mileage allowance for (part of) your commute to work paid out via pillar 2. The amount of the mileage allowance is then deducted from your federal mobility budget and paid net along with your salary.
This is fiscally very interesting because by spending budget in pillar 2, you avoid the special employee contribution of 38.07% that is charged when paid in pillar 3.
Moreover, thanks to the federal mobility budget, you can have not only your bike kilometers reimbursed but also the kilometers you travel on foot!
Concretely
€100 you spend in pillar 2 = €100 net on your paycheck.
€100 which you do not spend in the pillar 2 and which you therefore receive at the end of the year in pillar 3 = €61.93 net on your pay slip (after deduction of the 38.07% special employee contribution).