Liquid-transfer apparatus, and methodology employing the same, operatively interposable a syringe and a vial, and accommodating both a single-mouth-size (single-size), two-vial transfer procedure, and a two-mouth-size (two-size), two-vial transfer procedure. The apparatus includes a liquid-transfer device having a syringe-coupling end, a vial-coupling end, and liquid-passage structure effectively communicating between these ends. In the case of accommodating a single-mouth-size (single-size), two-vial procedure, only the liquid-transfer device is employed, and the same is sized with a vial-coupling end that is constructed for direct coupling to the top of the single-size vial which is used. In the case of accommodating a two-mouth-size (two-size), two-vial operation, the liquid-transfer device is employed along with a vial-coupling adaptor which is removably receivable in a connected relationship with the vial-coupling end in the device to adapt the same for coupling to the top of a vial having the smaller of the two sizes of vials which are to be employed. Under these circumstances, the entire procedure begins with coupling of the apparatus to a syringe and to the smaller-size vial, with the vial-coupling adaptor connected to the liquid-transfer device's vial-coupling end. Following a liquid-transfer operation with this smaller vial, the same is decoupled, and such decoupling automatically disconnects the vial-coupling adaptor and the liquid-transfer device. Thereafter, a vial of the larger size is coupled to the vial-coupling end in the liquid-transfer device, and a transfer procedure is completed between the syringe and the larger coupled vial.