Yes, you may-however, please note each Geni account requires an unique email address. Therefore, you will need to use a different email address then the one you are already using for your current account. Also, please note that if you invite someone to join your Tree who is already within another Tree, a Merge Invitation is sent on your behalf.
To start a new Tree, please visit: http://www.geni.com/family-tree/start . Also, please keep in mind that with multiple accounts, you will be required to delete your cookies between each login.
* Note: We do not recommend starting more than one tree, because the goal on Geni is to create a family tree of the world and this goes against our mission. Furthermore, you are not permitted to impersonate another person, so please make sure you are not violating our Terms of Service when creating a second account for your family.