There are tools that will generate a set of tests that cover every combination at least once without hitting all possible combinations (these work on the principle that most bugs will be surfaced by exercising pairs of settings).
Since the feature hasn't gone live, your business analyst is probably your best reference for the combinations that are most likely to be used. Depending on your customer base, you can probably start from the assumption that the feature will be most likely to be used with the default settings (Someone once did this - they asked Word users to send in their config files so they could analyze them and determine the most used options. What they found was that overwhelmingly most people went with the defaults).
From there, I'd look at settings that make sense for known users of other features: say you know that users of Feature A overwhelmingly have Application Setting X enabled. You also know that with Application Setting X, the new feature will only work with Feature Settings 1, 5, and 9 enabled. That's obviously a combination you need to cover.
Of course, if the new feature is independent of other application settings, that isn't relevant (with the caveat that I've found some really interesting bugs where settings should be independent and aren't...).
Without a pairwise testing tool to generate combinations, I'd analyze the settings myself as well, to try to determine the most likely to be used. After that, I'd look at building a set of tests that covers each setting in combination at least once. For on-off settings my starting points would be all on and all off, then a selection of on and off combinations.
For example, with four independent on-off settings A, B, C, D, I'd look at these mixes (in order, 1 is on, 0 is off):
This is pretty arbitrary and gets more... interesting when you have dependent settings and multi-valued settings. In those cases, I'd look to boundaries and dependencies as well.