How close can I plant a new Pygmy Date Palm to an existing one without damaging the roots?
You can plant it very close. I hesitate to say exactly how close without actually seeing the existing palm. Cutting some of the roots of your existing palm to plant the new palm is not a bad thing. You will not harm your existing palm by cutting some of its roots. Pygmy Date Palms have a very hardy,sturdy, and aggressive root system and it will repair itself soon after you plant your new plant. Right now is the best time to plant your new palm. Research has shown to plant palms at the beginning of the warm season to give them a long time to regenerate their root system.So bottom line you should pick a spot that you would want to plant your new palm and begin to dig. You will cut some roots and that is OK and as long as you are not cutting excessive numbers of roots you will be fine. Below is a link that may help you that explains some of the research to root damage when transplanting tress.
