testamentary trusts

Hi guys, not sure if this is the forum for this but is my best guess.

Can a testamentary trust with only one beneficiary, who is also the trustee, add other persons (ie the beneficiarys children) to the trust after the trust is enacted or prior to it being enacted, after the death of the person who set it up?

In order to enable more beneficiaries to spread the income for tax minimisation.

thanks for any advice.

TL