Doorbell chime has 2 wires attached to each terminal(screw)

Greeting, my doorbell chime has 2 wires connected to front terminal and 2 connected to transformer terminal (not 1 wire each) ? Is it ok to still attach the ring pro power kit 2 ? Also, If I want to bypass the mechanical chime, can I still do this with 2 wire setup (wires may not fit for the bypass connection) ? Any information will be greatly appreciated. Be safe !