From their reply brief:
The Senate Amici’s interest and arguments are distinct from those of the Appellants, as is apparent from any comparison of their briefs. The Senate Amici played a leading role in enacting the statutory provision at issue in this case, while the Obama Administration strongly opposed it. Without delving into the merits at this time, the Senate Amici seek to defend the fullest extent of Congress’s power under the Declare War Clause, as exercised in this instance, while the Appellants present narrower arguments that, if accepted, are likely to leave the extent of Congress’s power in doubt, even while winning this particular case. That the Senate Amici and the Appellants agree on some points, and on the ultimate disposition of this case, does not minimize the differences in their approaches and certainly does not render those approaches “identical.” Br. in Opposition (“BIO”) at 15.
My previous coverage is here, here, and here.