It is well known Esav sold his 'birthright' to Yaakov. Can a father decide arbitrarily which son he wants to favor as his bachor? If so -under what conditions?
If a father says "my bechor will not take double" or says "he will inherit like a regular son" it is invalid. It violates the commandment of not diverting inheritance Devarim 21:16
If the son agrees to give up his portion some permit it. Nesivos 281:6
See pischei choshen hilchos yerushah 4:6-8 for a complete discussion .
A firstborn's portion is unchangeable. A non firstborn may be increased since he is receiving an inheritance. A non inheriting relative (daughter among sons) cannot be set to receive an inheritance
The details for actually setting this up and possible workarounds such as writing a halachik will are complex and will often not be done properly without the assistance of professional halachik advisers (Business Halacha Institute and dinonline.org among others.)