What is the maximum altitude of the s1000+? It would certainly be crazy if it was lower than the inspire 1 or phantoms, considering those are quadcopters and the s1000+ is an octacopter.

Altitude limit is probably dictated more by flight time and than number of rotors.
Basically you have so many minutes to get up and then you have to get back down. Typically because of prop wash effect you cannot descend nearly as fast as you can ascend so of the cuff you may need to allocate maybe 66% of flight time to descending.
From a aerodynamic point of view I don't think you will reach a theoretical limit in the time you have to fly.
The extra motors buy you disaster avoidance by allowing you to fly with at least one motor out and protect your expensive camera and gear as well as provide additional safety.

From another point of view safety and ability to safely pilot you copter you probably don't want to test this.  suffice it to say all will fly high enough you cannot see them to pilot them and can go out of your standard radio control range.  It is probably illegal as well in most countries.

If you are talking about the maximum service altitude then I think that you are looking at about 10,000ft AMSL depending on the load.  Note that we are starting above 9,000ft.  I would never recommend that you fly that high as above 500ft you are in controlled airspace.

Just out of interest Ed - how is the performance at 9,000ft.  You obviously are dealing with less dense air than here (100ft) and have a reduced maximum lift. Service would nmean you have <100ft per minute lift ability.