Suppose you have two adult conjoined twins, Liz and Cat. A procedure exists that would remove Cat from Liz's body but would result in the death of Cat. Not perf

Suppose you have two adult conjoined twins, Liz and Cat. A procedure exists that would remove Cat from Liz's body but would result in the death of Cat. Not performing the procedure results in a significantly lower quality of life for Liz. Is it okay for Liz to knock Cat out, take herself to a hospital, and have the surgeon remove Cat from her body? Or should society force Liz to share her body with Cat? The opposing perspective would map this closer to the abortion debate than the blood transfusion scenario. I wonder myself which is more relevant and why I have such different responses to the two scenarios.