Safety is already a significant concern with 750V third rail, due to the risk of staff, passengers or trespassers receiving an electrical shock from the unshielded conductor rail. At 750V, a shock would be likely to cause serious but not lethal injuries. At 1500V, the likelihood of fatal injuries is already considerably greater.
For a given voltage, having a 4-rail system is not much safer than 3 rails, as you can still easily bridge the gap between the highest and lowest potentials by tripping and landing across the two conductor rails, for example. Having a fourth rail also makes it a lot easier for such a trip to occur, as the gap for your feet in the foot-foot is much smaller.
The ORR is already very cautious about 750V third rail - it is only legal because it is "grandfathered in" - so there is no way they would entertain any modification causing an increase in risk.
You could only really do it by introducing shielding such that the underside of the suspended, covered rail is live - as is done on many metro systems around the world, and for example on the DLR. Such an upgrade would be highly disruptive, and would never deliver acceptable cost:benefit ratios (bearing in mind the rather minor performance improvements that it would enable). Far better to switch to overhead electrification, if at all.