Yes, it is easily possible to get your RA28 handling well enough to accept greater power. A large number of aftermarket components exist that will make your car handle more than acceptably better. Examples:
Bushes from Superpro or Nolathane / Red Ranger.
Whiteline or Corona TT142 larger front sway bar.
Lovells or Kings springs
Koni or KYB shocks.
Whiteline rear sway bar.
There are many other bits available out there if you search hard enough for them.
Mitch.