Right now there is one socket holding a 75 watt flood light pointing
straight ahead. I need to keep that direction of light, but would
like to add some light above and below the currently lit area. Using
a twin in another twin doesn't allow me to get the right angles. I
have to climb up on a ladder in a difficult position to reach this
light, so I don't feel like trying to rewire in a different light
holder up there.

My mother doesn't live near me, so I can't take a picture to
illustrate the tripler for now, but it looks just like a twin adapter,
except one bulb is in line with the socket and the other two form a
larger angle with the socket than a twin.