The famous equation developed by Tsiolkovskii earlier this century says that:
V = c ln( (mc + mf + mm)/ (mc + mm) )where V is the velocity of the spacecraft, c is the exit speed of the propellants, mc is the mass of the spacecraft, mm is the mass of the rocket motor, and mf is the mass of the fuel. For most types of ion motors, c is in the range from 30 to 200 kilometers/sec and thrusts are about 0.0001g over months to years. As you can see from the formula, the only way to make V greater than c is for ln(m0/mf) to be greater than 1.0. This would require (mc + mf + mm)/(mc + mm) > 2.718 . In other words, if you could arrange for the initial weight including fuel to be more than 2.7 times greater than the final weight without the fuel you could get spacecraft speeds faster than propellant speeds. In other words, a 1 ton space craft with a 3 ton motor and 6.8 tons of 'fuel' would have an initial mass of 10.8 tons initially, and 4.0 tons after the fuel was used up and would achieve V = c. If you used 10 tons of fuel, then you would get ln(14.0/4.0) = 1.25 so that V = 1.25c.