Genetics limit everything. They limit our height, they make us susceptible to certain diseases, and they end up giving some guys small hands. Screw genetics. No guy wants to hear how effeminate or cute his hands are.
Its an uphill battle; past ~25 years old epiphyseal plates seal and bones stop growing longer. That means no your hands can’t get longer.
But there’s still hope. There are a number of muscle groups on the hand that facilitate lateral movement. Weightlifters often claim grip-straining exercises like double-overhand deadlifts and olympic lifts can induce myoplasmic hypertrophy to grow these muscles.
There’s also Wolfe’s law. According to wikipedia:
Wolff’s law is a theory developed by the German anatomist and surgeon Julius Wolff (1836–1902) in the 19th century that states that bone in a healthy person or animal will adapt to the loads under which it is placed. If loading on a particular bone increases, the bone will remodel itself over time to become stronger to resist that sort of loading. The internal architecture of the trabeculae undergoes adaptive changes, followed by secondary changes to the external cortical portion of the bone, perhaps becoming thicker as a result. The inverse is true as well: if the loading on a bone decreases, the bone will become weaker due to turnover, it is less metabolically costly to maintain and there is no stimulus for continued remodeling that is required to maintain bone mass.
tl:dr If you don’t use it, you lose it. But if you increase the loads you place your hands under, your bones will remodel itself to resist this kind of stress. Eventually through gradual changes, you can get thicker and larger hands.
Livestrong.com offers some exercises for loading stress on hands.
Of course there’s also hormone therapy. More on that in another article.