Can karma operate at the level of groups i.e. collectively?

The concept of collective karma also crops up in the Pāḷi commentarial tradition, though it is not called that.

Karma as we find it in the suttas is hardly unified, but generally speaking it is purely a matter of individual practice. But the theories of karma in the suttas don't seem to have survived in practice - every sect of Buddhism mucked about with the theories of the Pāḷi Canon because they are internally inconsistent.

In my first published article, Suicide as a Response to Suffering, on suicide in the Pāḷi Canon, I noted the example (SN 54.9) of the dozens of monks who committed mass suicide after being taught the meditation on the foulness of the body and the decomposition of the corpse by the Buddha. Now on face value this is a tragic mistake on the Buddha's part, and the tradition seems to have felt that it needed explaining. Buddhaghosa's commentary explains it with a story about the monks concerned being connected by a common fate. They had all lived together as hunters in the past. See Bodhi's Saṃyutta Nikāya translation, The Connected Discourses, p.1951, note 301. In this story the Buddha implausibly knows that the monks are going to commit suicide and can do nothing except relieve their attachment to their bodies, so that suicide is easier. This is all wildly implausible, but presumably Buddhaghosa felt it was better than admitting the Buddha had made a gigantic mistake.

"Collective karma" used to be a favourite subject for arguments amongst Buddhists in the early forms of internet social networking such as Newsgroups and Listservs. I never found such discussions very helpful.

Prof Richard Hayes (aka Dharmacārī Dayāmati) wrote a talk about it for his visiting professorship in Leiden in 2009. Is there such a thing as collective karma? Here he covers the ground pretty well, though he leaves the question of whether the idea has any real value open. Personally I don't see much value in it.

This is probably too long to post as a comment, but isn't totally an answer either, in any case it's something of a reference to this.

This summary is in reference to the commentary of the Dhammapada verses 21-23:

There was some king in the Buddha's time ( I don't remember which), whom had two Queen consorts. One of them was virtuous, the other evil and scheming. The virtuous one had a hand maiden who would buy flowers for her Queen every day, but stole from her in doing so.

The hand maiden would take the money the queen gave her for flowers, keep half the money, and return to the Queen only half as many flowers and she had ought to, the Queen not knowing any better. Until one day, this hand maiden heard the Buddha teach, attained stream entry, and then returned to the Queen, confessing her transgression.

The Queen was not mad, but impressed that the Buddha's teaching was this profound.

Fast forwarding, Ananda ends up coming to the palace to teach the Queen and her attendants, the evil Queen wanting to get rid of the good queen, as the evil queen had qualms with the Buddha due to a past misgiving, but was unable to get at him, plots against the good queen.

The evil queen ends up burning the good queen and her attendants alive in a bed chamber, although while they are burning to death they are able to be mindful and attain the path. It is explained in the sutta that the queen and her attendants suffered this kamma because of a misdeed they all committed in a past life.

They had started a fire in a field where a Pacceka Buddha was in a deep state of meditation. Because of this deep state of meditation, he was unharmed. But they not being aware of this, thinking he was burnt and dead, built another fire around his body to fully dispose of the evidence, and left him. The Pacceka Buddha was fine, but the weight of this action followed them all into this life, all of them suffering the same fate.