Yes you can do this, its accully quite simple.
1. you need a signal converter that will connect to all your speaker
wires, and give you a set of pre amp outputs, those u will need to run
to your amp.

You will need to position your amp where ever your goin to put it, with
a ford f350 I'd recomend running it under the front pasenger seat. its
open and easy to work under. make sure u mount it close to the back so
you can scoot your seat up and see it all. and then u will have to run
your power wire from your batterie to the amp, then on the other side
of your truck u need to run your RCA cables from the back of the head
unit to the amp. You dont want to run your RCA cable close to your
power cable because in some cases it is known to cause distortion.

2. Now is the tough part, you have to run a remote wire. This can prove
to be tough. Ok here we go.
A. Pull the panel off from under your stearing wheel accessing the
ignition.
B. Define the positive cable.
C. Cut the positive and strip both ends back about 1/2 an inch.
E. You need to connect a wiar splitter, they are little silver
connecters, u need to put the positive running from your batterie to
the end that there is only one entrance hole, crimp it down.
F. Now take the other end of the ignition wire and connect it to
one of the openings on the other side. Crimp it down
G. Now take the remote wire (most of the time blue. it will come in
your wire kit you'll need to buy for the amp) and crimp it on the last
open port.

Now you will need to figure out a way to hide that wire and run it to
your amp, it will connect to the REM teminal.

Bottom line the hard part will be splicing a wire to use as a remote
(rem) for your amp, you dont have to do it to the ignition, but it is
one of the only things that turn on when your motor is started. You can
go through your fuse box but that is extremly complicating...