If none of the prepackaged solutions work out, I would have to write my own PIM suite. Key features would be:
Supports contacts, calendar, tasks and notes, but no native e-mail management.
Multi-user access to the objects.
Network service to wild-side clients.
The server needs to use existing popular protocols to interact with the client, so a choice of client software can be used. RFC 2425 and RFC 2445, called iCalendar, vCard, etc., are recommended for the wire format, and WebDAV (HTTP extension) is commonly supported for the session protocol, under the name CalDAV. Since credentials (passwords) and privacy-regulated data are exchanged, the communication must be encrypted, and SSL/TLS is the credible encryption initiation framework.
The server also must provide an all-web interface accessible on any web browser, to give access to hosts on which PIM client software cannot be installed.
The client installation needs a local proxy server that caches relevant PIM objects for use when the network is not available, but the server copy is authoritative. Alterations made in the cache should propagate back to the server when available. The proxy must use the local protocol expected by the e-mail reader and other programs; e.g. on Android and KDE there is a D-Bus protocol The proxy should also provide special-purpose local web service, obviating a dedicated local UI.
Transitive authentication or single sign-on: whatever facilities the underlying operating system provides, the program should use them to gain access to the server. In particular, if the client has a Kerberos credential the client should send it in and the server should honor it.
Client support on at least desktop Linux, Android, iPhone and Windows.
Storing the PIM objects in the owner's home directory is most preferred.
It must be possible for an individual user to extract selected PIM objects in a popular interchange format (RFC 2445), for mailing or for backup. It must be possible for such files to be imported, if received as attachments, or for migration, or for disaster recovery. It must be possible to back up and restore everyone's PIM objects in bulk, preferably in textual form so in case of software errors they can be cleaned up.
The targeted organizations have never used Microsoft Exchange, so Exchange coordination is not important. But other people installing PIM suites may have a major need to migrate from Exchange, Google Apps, etc., or to federate with neighbors who use these suites.
Here are some possibilites for the name of a newly written PIM suite. The trigram PIM occurs in only 75 words in /usr/share/dict/words (out of 3.6e5), mostly in word families. Here is a list by family: