Yes, it is possible to share an editable version of an XLSForm template with members from a different organization without affecting the existing survey data in ArcGIS Survey123. This article provides three workflows to share an XLSForm template with members from different organizations.
Note: Download the XLSForm of the survey through ArcGIS Survey123 Connect if the existing survey form is created through the Survey123 website.
Share the XLSForm through email
Share the XLSForm through an email to the members of other organizations. This allows only the selected members of an organization to access the XLSForm template. Refer to ArcGIS Survey123: Can I import existing XLSForms? for more information.
Create a group and invite members to the group
In ArcGIS Online, create a group and invite the members to join the group. After the group is created, add the XLSForm to the group to allow the members of the group to access the XLSForm. Refer to ArcGIS Online: Create a group and ArcGIS Online: Share items with a group for instructions.
Upload the XLSForm and share it publicly
Upload the XLSForm to ArcGIS Online and set the sharing level to Everyone (public) to allow members of an organization and outside of the organization to access the form and use it as a template. Refer to ArcGIS Online: Share items with everyone for instructions.