This thought just came to me, and I wasn't able to dig up an answer in the rules, but I suppose it is mega likely I simply missed the entry.
How many times can a single card trigger a response? I think the perfect example for my question might be something like Pentos.
If I have three Targ characters out, and they all have attachments, and someone plays Valar, can I save each of them, each individually triggering Pentos' response and discarding an attachment to save them? Or can I only do it once within the confines of resolving Valar?