Can I run a single Magento for DACH (Austria + Germany + Switzerland)?

Yes, and you almost certainly should. ~80% of Austrian merchants we work with want at least AT + DE coverage from day one, and many add CH within a year. Magento’s multi-store architecture handles this cleanly:

• Single Magento backend, 3 stores, AT (yourbrand.at), DE (yourbrand.de), CH (yourbrand.ch). Shared catalogue, separate URLs.
• Per-store currency, AT + DE in EUR, CH in CHF (live FX or pinned rate).
• Per-store tax, AT USt 20% (13% / 10% / 0% reduced), DE MwSt 19% (7% reduced), CH MwSt 8.1% (2.6% / 3.8% reduced). Each with separate tax_zone rules.
• Per-store payment methods, AT adds EPS + RatePay, DE adds giropay + RatePay, CH adds TWINT + PostFinance + Reka. PayPal + Apple Pay + cards across all three.
• Per-store shipping, AT: Österreichische Post + DPD AT + GLS AT. DE: DHL + DPD DE + Hermes. CH: Swiss Post + DHL Express.
• Per-store legal pages, AGB + Datenschutz + Impressum per country. DSG-A enforces in AT, BfDI in DE, EDÖB in CH.
• Per-store language, all three share Hochdeutsch (the default), but AT prefers Jänner over Januar, Marille over Aprikose, Topfen over Quark. We add an Austrian-German locale override on top of de_DE so the AT store gets the right vocabulary.