And Saturn V wasn't some ultimate ideal space vehicle. It was big, but the F-1 engines were rather low performance. And all the material choices were made based on what was available at the time, many of which may have to be substituted, the designers didn't have the benefit of modern computer modeling, etc.
Just comparing kerosene engines...
The Rocketdyne F-1 got a sea level specific impulse of 263 s (exhaust velocity 2580 m/s), and a thrust to weight ratio of something like 75.
The RD-170 used for the Energia used an advanced staged-combustion cycle and got 309 s (3030 m/s) at sea level with a thrust to weight of 82.
The just-qualified Merlin 1D uses the simpler gas generator cycle of the F-1, but gets 282 s (2730 m/s), higher than any other gas generator engine. It has a much higher thrust to weight ratio: 150. It's rather smaller, but they're working on larger engines.
Overall vehicle mass fraction shows similar improvements. And the Saturn V was all built to 1960s standards in terms of electronics and instrumentation, and none of it was designed for modern manufacturing techniques. Just getting the mechanical stuff converted over to modern CAD/CAM systems would be an enormous effort. You're really better off starting from scratch.