the 707-320C historically operated at some high altitude airports (such as ZULS), and at their altitude, the APU cannot provide enough bleed air to spool up the engines (N2 does not budge).
There was a system on 707s that can rectify this issue; high pressure air bottles. These bottles are fitted to engines 2 and 3, and are charged to a minimum of 2700PSI, allowing engine starts even if the APU is insufficient (engines 1 and 4 can be started via crossbleed)
Although the manual states that the APU deprecated high pressure starts, this case will still benefit from it.