Yes it's entirely possible to have 3 DC-10's at NZCH at the same time.
Even though it is indeed, quite an un-likely, rare occasion to have them all captured at the same time in the aerial photo.
A likely scenario could either be to do with re-positioning for inter-connecting flights between Arrival and Departure resulting in a cross-over period or perhaps a overnight "lay-over", engineering and maintenance re-positioning etc, even a potential for a NZAA destination arrival flight that encounter bad weather, such as low level sea fog rolling in over the Manukau Harbour on arrival at NZAA (that has been known to happen from time to time, temporarily closing NZAA Airport to Air Traffic) resulting in an Alternate Fuel Reserve, Diverted, re- route flight to NZCH (who knows it's anyone's guess) with any number of possible scenario conclusions that could be inferred from the photo.
Since the following paragraph was found in this link about
Christchurch Airport"During 1963, the main runway was extended 427m southwest to 2,442 metres, providing for commercial jet operations. In April 1965, scheduled Boeing 707 jet services started, by Qantas to Sydney. Later in 1966, an international wing was added to the domestic terminal. In October 1968, NAC operated its first Boeing 737 to the airport. SAFE Air introduced a Chatham Island air link to Christchurch in December 1969. In 1972 the north-west runway was completely resealed and repainted. The first scheduled Boeing 747 service arrived on 3 December 1972, a Qantas flight from Sydney. Air New Zealand introduced its DC-10 aircraft to trans-Tasman services at the end of October 1973."
With all this in mind, it's highly likely that the Air New Zealand DC-10s had the following historic Trans Tasman routes across the Tasman Sea to the Australian cities of Melbourne and Sydney from Christchurch International NZCH South Island Hub along with re-positioning flights of the DC-10 aircraft fleet with Main trunk Domestic Passenger flights to and from the main Auckland International NZAA North Island Hub.
A possible scenario for the Air New Zealand circa 1970's early 80's DC-10s flights in and out of NZCH are Trans Tasman Australian historic sector routes for Melbourne YMML
NZAA - YMML - NZCH - NZAA
NZAA - YMML - NZCH
NZCH - YMML - NZAA
NZAA - NZCH
NZCH - YMML - NZCH
NZCH - NZAA
A possible scenario for the Air New Zealand circa 1970's early 80's DC-10s flights in and out of NZCH are Trans Tasman Australian historic sector routes for Sydney YSSY
NZAA - YSSY - NZCH - NZAA
NZAA - YSSY - NZCH
NZCH - YSSY - NZAA
NZAA - NZCH
NZCH - YSSY - NZCH
NZCH - NZAA
If you're interested in a further insight, into the Air New Zealand DC-10s suggest either reading the following from.
Air New Zealand - Flight Engineer, Gary Sommerville’s written detailed perspective of our DC10-30 era in his pdf document
DC-10-30 Experience. February 1974 - March 1981.Or watch his 27 minute historic slide show tribute showcasing each of the eight Air New Zealand DC-10s and find out what happened to them after retiring from their operational service with Air New Zealand in his
DC-10-30 Remembered video.