can many magi cooperate to open the arts?

Well, apprentices with major supernatural virtues could have had their Arts opened by a magus from the Line of Pralix. The Parens need to open the arts of his apprentice personally.
However with the use of a lab and all relevant rules for this the magus opening the arts of an apprentice with previous mystical knowledge has a cart load of ways to boost his lab total. Even though Covenants does not list 'opening the arts ' as a lab activity for specialization you still get Aura and Gen Quality added, plus Familiars, plus any In and Vi specializations.

Also consider, that there are several activities that require a lab without needing a lab total generated: Fixing ACs was mentioned earlier, but also a Vis Transfer (ArM5 page 95), and last but not least Preparing for Enchantment - this last one does not need any specific lab total to do, only the requires Magic Theory score to use the relevant amount of vis. Oh, and also Items of Quality from Verditius Mysteries.

But I can't remember a single thing that uses a Lab Total but explicitly does not require a lab. Which is why Opening the Arts does indeed sound like a Lab Activity. Even though an apprentice without supernatural knowledge doesn't require even a lab total of 0 and therefore by leap of logic no lab.