Objective: Uncertainty exists regarding optimal supplemental diet for very preterm infants if the mother’s own milk (MM) is insufficient. We evaluated feasibility for a randomised controlled trial (RCT) powered to detect important differences in health outcomes. Methods: In this open, parallel, feasibility trial, we randomised infants 25+0–31+6 weeks of gestation by opt-out consent to one of three diets: unfortified human milk (UHM) (unfortified MM and/or unfortified pasteurised human donor milk (DM) supplement), fortified human milk (FHM) (fortified MM and/or fortified DM supplement), and unfortified MM and/or preterm formula (PTF) supplement from birth to 35+0 weeks post menstrual age. Feasibility outcomes included opt-outs, adherence rates, and slow growth safety criteria. We also obtained anthropometry, and magnetic resonance imaging body composition data at term and term plus 6 weeks (opt-in consent). Results: Of 35 infants randomised to UHM, 34 to FHM, and 34 to PTF groups, 21, 19, and 24 infants completed imaging at term, respectively. Study entry opt-out rate was 38%; 6% of parents subsequently withdrew from feeding intervention. Two infants met predefined slow weight gain thresholds. There were no significant between-group differences in term total adipose tissue volume (mean [SD]: UHM: 0.870 L [0.35 L]; FHM: 0.889 L [0.31 L]; PTF: 0.809 L [0.25 L], p = 0.66), nor in any other body composition measure or anthropometry at either timepoint. Conclusions: Randomisation to UHM, FHM, and PTF diets by opt-out consent was acceptable to parents and clinical teams, associated with safe growth profiles and no significant differences in body composition. Our data provide justification to proceed to a larger RCT.