Digital transformation is often framed as a strategic, top-down initiative to ease the growing strain on healthcare, reflecting overly optimistic digital government narratives. However, this perspective neglects the infrastructural realities of digitalization within a fragmented, complex technological landscape. Challenges that intensify when trying to shift toward open-ended goals like person-centred care (PCC). This study addresses this gap by exploring infrastructuring as the often-invisible work of healthcare professionals. Despite its significance, a microlevel view of infrastructuring remains underexplored. Based on empirical research on digital triage and virtual consultations in primary care, the findings reveal how clinicians enact infrastructuring as both innovative and compensatory tinkering, which are interleaved. Furthermore, a paradox is exposed: while technology is promised as malleable, clinicians experience a rigid digital infrastructure. Consequently, the paper introduces the Tinkering Triad, a framework emphasizing engaged employees, adaptive governance, and flexible digital infrastructure as key enablers for tinkering and thus digital transformation and PCC.