Can a TRIS be added to by way of contributions or roll-over once it has commenced?

No.  Once a TRIS has commenced, the superannuation law provides that the capital supporting the TRIS cannot be added to by way of contribution or roll-over.

Contributions can continue to be made for the pensioner after the TRIS has commenced, however, they would be paid into a separate accumulation account for the pensioner, rather than into the pension account.