Hi.
I use DAVdroid and SOGo with my colleagues.
We noticed that same events in multiple calendars are only displayed once in Android.
Example :
I (Damien) have invited a colleague (Christian) to a “Test” event at 18 and he accepted it.
My calendar is in black in SOGo, Chistian’s calendar is in grey :

We have the same thing in Thunderbird (with SOGo connector/integrator) (Christian’s calendar in blue) :

But on my Android phone (in S Planner app and also Google Calendar app), my “Test” event is not displayed :

Sometimes, after resync, the event is swapped : only my “Test” event is displayed and not Christian’s event.
It’s a very simple event (no recursion, etc.), here is the ICS file (from my calendar) :
BEGIN:VCALENDAR
PRODID:-//Mozilla.org/NONSGML Mozilla Calendar V1.1//EN
VERSION:2.0
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19700329T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19701025T030000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CREATED:20150602T104041Z
LAST-MODIFIED:20150602T104055Z
DTSTAMP:20150602T104055Z
UID:ef62d894-872b-4931-a428-498663af506c
SUMMARY:Test
ORGANIZER;PARTSTAT=ACCEPTED;ROLE=CHAIR;RSVP=TRUE;CN=Damien:mailto:
damien@xxx.fr
ATTENDEE;PARTSTAT=ACCEPTED;ROLE=REQ-PARTICIPANT;CN=Christian:mailto:
christian@xxx.fr
DTSTART;TZID=Europe/Paris:20150603T180000
DTEND;TZID=Europe/Paris:20150603T190000
CLASS:PUBLIC
X-MOZ-GENERATION:2
TRANSP:OPAQUE
SEQUENCE:1
END:VEVENT
END:VCALENDAR
Here is the ICS from Christian’s calendar :
BEGIN:VCALENDAR
PRODID:-//Mozilla.org/NONSGML Mozilla Calendar V1.1//EN
VERSION:2.0
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19700329T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19701025T030000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CREATED:20150602T104041Z
LAST-MODIFIED:20150602T104911Z
DTSTAMP:20150602T104911Z
UID:ef62d894-872b-4931-a428-498663af506c
SUMMARY:Test
ORGANIZER;ROLE=CHAIR;PARTSTAT=ACCEPTED;CN=Damien;RSVP=TRUE:mailto:
damien@xxx.fr
ATTENDEE;ROLE=REQ-PARTICIPANT;PARTSTAT=ACCEPTED;CN=Christian:mailto:
christian@xxx.fr
DTSTART;TZID=Europe/Paris:20150603T180000
DTEND;TZID=Europe/Paris:20150603T190000
CLASS:PUBLIC
X-MOZ-GENERATION:3
TRANSP:OPAQUE
SEQUENCE:1
END:VEVENT
END:VCALENDAR
I use Android 4.4.4 and DAVdroid 0.8.0.