From the SFSRD on Adamantine (emphasis mine):
Adamantine is a starmetal... Pure adamantine is exceedingly rare and expensive, so weapons using adamantine are always made of an adamantine alloy. Weapons or ammunition fashioned from adamantine alloy overcome the damage reduction... Weapons and ammunition without metal parts can’t be made from adamantine alloy.
From the SFSRD on Cold Iron:
Cold iron is... Weapons or ammunition fashioned from cold iron overcome the damage reduction... Weapons or ammunition without metal parts can’t be made from cold iron.
From the SFSRD on Silver (emphasis mine):
A complex process involving alchemy, magic, and metallurgy can bond silver to weapons or ammunition so that they overcome the damage reduction of... The silvering process can’t be applied to nonmetal items, and it doesn’t work on rare metals such as adamantine, cold iron, or starmetals.
Silver weapons explicitly cannot also be adamantine, cold iron, or other starmetal-based special materials. Adamantine and cold iron do not spell out similar restrictions, and adamantine even explicitly says the weapon is made of an alloy that simply includes adamantine.
Can a weapon be made of an alloy of adamantine and cold iron and gain both benefits?