There are really two aspect to this :
1) Will increasing roll stiffness improve handling to an extent which offsets any increase in weight by adding extra chassis members ?
2) If yes what is the best strategy for improving the stiffness of the chassis.
The issue here is that this is a fairly simple ladder chassis so we are really looking at creating some sort of ladder/spaceframe hybrid. However we also need to consider that fact that the rear suspension is pretty basic in the form of longitudinal leaf springs so there is no guarantee that stiffer is better without identifying specific characteristics which you need to improve. Eg increasing rear roll stiffness isn't necessarily better unless this is identified as a limiting factor on performance.
In some ways it might be a more productive exercise to investigate where you can loose weight by removing materiel form the exiting chassis by identifying areas where it is under-stressed. Apart form anything else this should definitely give some easily quantifiable benefit.
In terms of an assignment it may also make more sense to demonstrate how a space-frame chassis could give the same torsional stiffness for less mass. 333
Again this give your project a much more well defined objective.
For example if you manage to find a way to make the existing chassis 10% stiffer it is then very hard for you to show what real world performance benefits this gives without actually carrying out the modifications and testing them. On the other hand if you can make it 10% lighter for the same stiffness that is a very obvious benefit.
I would also add that having a project with a well defined strategy for improving a design is fundamentally better than just changing some arbitrary design parameter without any clear idea of how it will improve performance.
So project titles like 'A worked example of the weight advantages of a space-frame vs ladder chassis' or 'Reducing the weight of an MGA chassis' will make much more sense to an engineering professor than 'Showing that adding more mass to a structure can make it stiffer'.
Eg say you make it 10% stiffer and 10% heavier...is that better ? Unless you can prove it is better the whole exercise is a bit pointless. If it was an experimental exercise things would be a bit different.
The point here is that is any scientific and engineering experiment you need to be able to reach some conclusion. If your intended approach didn't work that is fine as long as you can say that it didn't work and why what is bad is when there is no way to tell withing the scope of the project whether it was worth doing or not.
Eg 'I investigated whether it was practically possible possible to lighten the chassis of an MGA using the following strategies but none of the approaches I used were effective' is useful information.
However 'I made the chassis of an MGA 10% stiffer by increasing its mass by 10%' doesn't really tell you anything useful, unless you can add further information how this improves its performance.
As an aside there is also the fact that for classic cars (in th e UK at least) any marginal increase i performance has much less value attached to it than preserving its authenticity and originality. 441