I'm afraid you've lost me..... all I can say is velocities are directly additive as long as the craft's velocity is <<"c" (speed of light), but not as you approach light speed.
An additional consideration is the increase in apparent mass as the velocity approaches "c" -- this requires vastly increasing expenditures of energy (read: fuel) to obtain the same incremental increase in velocity.
IOW, it takes virtually an infinite amount of fuel to accelerate an object having mass to a velocity="c", because the apparent mass ---> infinity as "v" ---> "c."
Also, if you look at a typical 3-stage rocket, the first stage is enormous. It's almost all fuel, the purpose of which is to get the next two stages off the ground. If you had a 50-stage or 100-stage rocket to do what you suggest, I shudder to think how big the first stage would have to be in order to lift the others. In other words, if the ship carries its own fuel, you're unlikly to get very far with your project. It will have to await a whole new propulsion system. And even then, as longshadow says, you can't achieve lightspeed even if you had an infinite fuel supply.
I know there are problems with size,weight,fuel capacity but is the possibility real.It may not be possible for reasons I`m not knowledgeable enough to see but still am curious.
Yo momma's so fat she's gotta Schwarzschild radius.