Yes, if you wish. If you appoint a second trustee, when setting up the trust they will get full disclosure of the assets in the trust. They will also have to be part of the decision making with future assets. If it is a small trust, meaning it doesn’t have much in the way of assets or activity, then perhaps a second current trustee is not even needed. A second current trustee may be more merited if the trust has a lot of activity and needs more officers to assist. Or a second current trustee could be desirable if the primary trustee has a colleague, business partner, or friend with whom he or she wishes to work and share control. The second trustee has to be non-family-related to the primary trustee.
But, if there is no second current trustee, then there absolutely MUST be a successor trustee. Having a successor trustee is a good idea anyway, sometime . . . because what would happen if the existing trustees leave this Earth or otherwise resign or become unavailable? Then the trust is orphaned and left adrift upon the sea. So, whenever convenient, each current trustee should have a successor trustee appointed . . . a trustee to take over if and when the current trustee is no longer serving the role.
If there are two current trustees, then it is not as urgent to have a successor trustee. But if there is only one current trustee, then it is mandatory to have a successor trustee appointed immediately. The banks will require this, if a bank account is to be opened for the trust.