TAP Portugal, the national airline of Portugal, was founded in 1945 and was originally from the acronym of Transportes Aéreos Portugueses. TAP has been nicknamed with the backronym (back acronym) “Take Another Plane” since at least 1984 and “Try Another Plane” since at least 1987.
 
   
Wikipedia: TAP Portugal
TAP Portugal, founded 1945 as Transportes Aéreos Portugueses, SGPS, S.A., commonly known as TAP, is the national airline of Portugal. TAP Portugal is 100% state owned and has its head office in Building 25 on the grounds of Portela Airport in Santa Maria dos Olivais, Lisbon, and has been a member of the Star Alliance since 14 March 2005, the same day on which the company celebrated its 60th anniversary. Its hub in Lisbon is a key European gateway at the crossroads of Africa, South America and North America. Privatisation of the airline will be under way in 2012 as part of Portugal’s €78 billion bailout agreed by the EU and the IMF.
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TAP originally meant Transportes Aéreos Portugueses (Portuguese Air Transportations). This was dropped in 1979 when the company changed its name to TAP Air Portugal, then dropped again to its current operational name, TAP Portugal.
 
Google Books
Empire of the Sky:
The Politics, Contests and Cartels of World Airlines
By Anthony Sampson
New York, NY: Random House
1984
Pg. 95:
The Portuguese TAP was sometimes unpredictable (“Take Another Plane”) but outstandingly safe, and like Alitalia and Iberia it found new scope in Latin America.
 
13 June 1987, Lethbridge (Alberta) Herald, “Air travel passengers playing name game” by David Gersovitz (The Canadian Press), pg. C5, col. 2:
TAP of Portugal naturally lends itself to Try Another Plane.
 
Google Books
European diary, 1977-1981
By Roy Jenkins
London: Collins
1989
Pg. 576:
Jennifer’s plane from London was rather later than mine and during the wait ‘Mrs Si Carneiro’ enlivened proceedings by expressing distrust of TAP (Portuguese Airlines) and asking me if I knew that the initials were known (by whom?) to stand for ‘take another plane’.
     
Google Groups: alt.tasteless.jokes
AIRLINERs’ INITIALs
yelserP .A sivlE
8/27/93
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TAP Take Another Plane
   
California Academy of Sciences—Gulf of Guinea Islands Biodiversity Project
SNAKES, TARANTULAS, DIATOMS, & DINNER
Dispatch Number Seven - May 9, 2001
Text by Fabio Penny, Computer Services
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TAP, (affectionally referred to as Take Another Plane), apologized for the misinformation we were given, but all we wanted to do was confirm Sarah’s arrival.
 
Google Books
One Man’s Africa
By John Ryan
Johannesburg: John Ball
2002
Pg. 321:
Many still maintain the acronym of their national carrier, TAP, stands for ‘Take Another Plane’.
 
Google Books
Frequent Flyer Humor and One-Upmanship
By George W. Stewart
Indianapolis, IN: Dog Ear Publishing
2011
Pg. 65:
TAP (Portuguese Air) — Take Another Plane