Would the collective noun for the Ivanovic family be "Ivanoviches"?
I called the Invanoviches for confirmation.
I think few would have a problem with that sentence if it were spoken aloud. But in writing, it's unlikely that the spelling "Ivanoviches" would be recommended by any mainstream source.
From Hellion's answer to a somewhat similar question (plural of 'Davidovici'):
The Chicago Manual of Style recommends that when a plural form suggests a false pronunciation, the name is best left unpluralized. (Preferably this would be done by recasting the sentence to avoid the need for pluralization.)
If you must pluralize a name that is spelled Ivanovic and pronounced with /tʃ/ (the ch sound of rich) as the last sound, the plural will presumably be regularly formed, and so pronounced with /tʃɨz/. As RegDwigнt♦ said in the comments, -hes is not a standard spelling of the regular English plural ending, so "Ivanoviches" is out.
The regular English plural ending is standardly spelled as either -s or -es, normally depending on the spelling and pronunciation of the word. For example, nouns ending in ch and pronounced with /k/ are spelled with -chs /ks/ (e.g. stomachs), but nouns ending in ch and pronounced with /tʃ/ are spelled with -ches /tʃɨz/ (e.g. beaches).
But the usual alternation between -s and -es has at least one well-known exception for proper nouns: proper nouns ending in a consonant letter + -y often pluralize as -ys, even though common nouns ending in a consonant letter + -y regularly pluralize as -ies. The existence of that exception shows that we can't necessarily assume that the same rules apply to the spelling of plural common nouns and plural proper nouns. So even though the use of -s vs. -es is based on pronunciation for common nouns spelled with -ch, such as stomachs and beaches, the spelling pattern could be different for proper nouns ending in -c.
So I don't think there is any clear way to establish whether Ivanovics or Ivanovices is preferable. (However, the spelling Ivanovic's would presumably be rejected for containing a "greengrocer's apostrophe".)
I thought it might be useful to add some real examples of the spelling "Ivanovices" to this post to show that it is not just a theoretical invention. I admit that these examples are taken from sports writing, which is not known for perfect adherence to "standard" English:
Who will REALLY regard it as a big deal if Ivanovic or Jankovic does well in the Asian autumn swing? [...] Let’s acknowledge this about the Ivanovices, Jankovices, and Nishikoris of the world: They’re making a great living off tennis.
("Seeds of Discontent and the Search for Identity in Tennis", by Matt Zemek, Aug 31, 2015 19:57, Attacking the Net)
instead of yet another list populated by the Sharapovas and the Wozniackis and the Ivanovices—some of the most googled female athletes in the world—I decided to a do a list of gorgeous tennis players at the Aussie Open that you’ve never even heard of.
("15 Gorgeous Women You've Never Heard of at the 2012 Australian Open", by Esteban, TotalProSports.com)
With all the Sharapovas and Ivanovices that are emerging in women's tennis, how many more big tournament wins are in the cards for the sisters?
(transcript of Tony Cox in "Shaquille Attacks Kobe with Raunchy Rap", NPR News & Notes)
Wiktionary does not provide a plural for the Serbo-Croatian surname Ivanovic.
In January 1994, Igor and Ludmilla Ivanovic opened the doors of their bakery, … . The Ivanovics must decide how to reconfigure the leadership structure of the company without losing their control over the fundamentals. (Gendron, Harvard Business Review) --emphasis mine.
The Ivanovics lived in a modest weatherboard home in Brunswick. (Shand, Big Shots, Accessed from GoogleBooks.) --emphasis mine.
To add to the woes, Ivanovics is also a surname.
plural of Ivanovich
Ivanovich (plural Ivanovichs or Ivanoviches)