JavaScript (ES6), 74 71 bytes
Thanks to @tsh for identifying 2 useless bytes that were used to fix a bug
Saved 3 bytes thanks to @tsh
f=([a,...r],k,i=1)=>a?Math.max(...a.map(n=>k&(i+=i)?-1/0:n+f(r,k|i))):0
JavaScript (ES6),
Arnauld
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