WARNING: this is quite complicated and techie. You must fully understand what you’re doing. If accept, then read on.

As some of us (users) already succeeded to sync with Google Contacts and Google Calendar, there is one serious limitation: one calendar per sync account.
Though DAVx5 GUI doesn’t allow adding more calendars, low-level hack indeed is able to accomplish that.
HOWTO:

  1. in the Android device use sqlite to access the services.db. You need root:

sqlite /data/data/at.bitfire.davdroid/databases/services.db

  1. take a look at the contents:

.dump

  1. find the calendar entry in the “collection” table (INSERT statement)
  2. change some fields to deal with another calendar:

INSERT INTO “collection” VALUES(55,5,‘CALENDAR’,‘https://www.google.com/calendar/dav/********%40group.calendar.google.com/events/’,1,1,0,‘AnotherCal’,'AnotherCal’,NULL,'BEGIN:VCALENDAR
PRODID:-//Google Inc//Google Calendar 70.9054//EN
VERSION:2.0
CALSCALE:GREGORIAN
X-WR-CALNAME:AnotherCal
X-WR-TIMEZONE:Asia/Almaty
BEGIN:VTIMEZONE
TZID:Asia/Almaty
X-LIC-LOCATION:Asia/Almaty
BEGIN:STANDARD
TZOFFSETFROM:+0600
TZOFFSETTO:+0600
TZNAME:+06
DTSTART:19700101T000000
END:STANDARD
END:VTIMEZONE
END:VCALENDAR
',1,0,0,NULL,1);

  1. push this INSERT statement to sqlite
  2. restart DAVx5

Calendar ids obtained from that calendar Settings.
Good luck! and be careful.