Piper management wanted a simplified, inexpensive, six-seat multi-engine airplane and actually considered going with a three-engine, fixed-gear, fixed-prop configuration.
This was the original prototype PA-32 airframe (N9999W) with a 250-hp Lycoming in the nose and (initially) 115-hp engines in the wings (later swapped for 150-hp engines).
Gotta think that engine-out performance was nothing to write home about. That looks like the original PA-32 vertical tail, and an inop engine with fixed-pitch prop would certainly create an awful lot of drag (a la Champion Lancer).
The idea of three engines might have had some appeal when this prototype first flew in 1965, in the era of cheap fuel and (relatively) cheap maintenance, but it certainly seems goofy today. Piper finally gave up on the three-engine idea and re-worked the basic airframe into the twin-engine PA-34 "Twin-Six" (fixed gear, 180-hp engines), which ultimately morphed into the Seneca.