Der Ort, an dem Jhwhs Name wohnt Eine oder mehrere Stätten?

Does the deuteronomic formula »the locality where Yhwh places his name/made his name to dwell« specifically indicate number (one place), or does it carry generic significance (such places generally)? In 1 Kings 18, MT implies a numerical meaning, whereas LXX implies a generic one. LXX may be more original in this respect.