Technically you'd put the objects in DMAMEM, not the class. Here an example: c1 lives in ITCM, c2 lives in DMAMEM and c3 in FLASHMEM
class myClass
{
public:
unsigned i = 42;
};
myClass c1;
DMAMEM myClass c2;
FLASHMEM const myClass c3;
void setup()
{
while (!Serial){ }...