This paper proposes a practice-derived 2×2 classification matrix for healthcare system design built on two operational axes: Acuity (Acute vs Non-Acute) and Delivery Modality (Interventional vs Non-Interventional). The resulting four quadrants - Acute Non-Interventional (Q1), Acute Interventional (Q2), Non-Acute Non-Interventional (Q3), and Non-Acute Interventional (Q4) - each carry distinct implications for facility location, workforce design, digital delivery architecture, financing, and cluster development. Healthcare systems worldwide are planned, financed, and regulated around a classification framework - the primary, secondary, and tertiary tier system - that was conceptualised in 1920 and formalised at Alma-Ata in 1978. Despite its ubiquity, this framework systematically fails to answer the questions most material to health system planners: where should a facility be located? What infrastructure does it require? Which services can be delivered digitally? How should financing be structured? The framework proposed in this paper emerged not from theoretical exercise but from fifteen years of operational healthcare system design and implementation across eastern and northern India, encompassing more than 1,100 hospital beds across West Bengal, Uttar Pradesh, Bihar, and Odisha. Repeated operational observation revealed that two variables - time sensitivity (acuity) and infrastructure dependency (intervention requirement) - are far more predictive of planning requirements than institutional hierarchy or medical specialty. A 2×2 classification matrix built on these two axes yields four operationally coherent quadrants, each with distinct implications for facility location, workforce, digital delivery architecture, financing design, and cluster development. The framework's larger thesis is that healthcare infrastructure should be organised according to operational systems logic rather than institutional tradition or specialty hierarchy.