In general, there is nothing to my knowledge that prohibits an LLC from acting as trustee. However, I question the wisdom behind doing that. You should probably consult an attorney before designating an LLC as trustee of your family trust.
My response is informational only. It is not meant as legal advice and is not meant to create an attorney-client relationship.
Consult an attorney who is experienced in forming asset protection trusts. It is highly complicated and you do not want any adverse tax consequences.
This is not legal advice and does not create an attorney-client relationship. This is not legal advice, it is only legal information. You should consult an attorney if you have any questions regarding this matter.
An LLC may serve as trustee, but the most important aspect of nominating a trustee is someone that you trust. Most LLC's are managed by one or a few individuals, so why the desire to name an LLC and not those individual managers directly? The potential consequences far outweigh any benefit this offers. Serving as trustee is a personal relationship, it is much better handled by a natural person.