Since Asana has its limitations when it comes to quoting text and threaded replies (those simply don't exist there), for more complex discussions we have decided to use Discourse, as it is specifically designed to handle long-term discussions with multiple partners and a potentially complex reply structure.
Slack comes with its own caveats -- while it offers a single reply-thread per initial post there is no more complexity available beyond that, and additionally Slack does not lend itself well to conversations that are expected to be carried on over the current day, as slack is a more or less synchronous medium.
Familiarize yourself with the categories and the fine-grained options to "watch" any of those categories (see upper right (!) icon in any category).
Watch any categories you like/will likely need for your work.
To clearly separate concerns, create a new topic rather than hijacking an existing one.
Put your topic in the appropriate category and apply helpful tags.
Take enough time to formulate your topic/reply, as it is more important for your text to be understandable and complete than to be available quickly.
Refrain from using humor/sarcasm/trolling in Discourse discussions as this can quickly derail the conversation in progress.
When abstracting anothers argument use the quote function to reproduce the argument you are abstracting, so as to avoid accidentally strawmanning their argument.
Present well structured arguments, to make it easy for others to follow and address your argument.