A follow-up question does not always require a completely new answer. Often it changes one assumption, asks for stronger evidence, or tests whether you understand the trade-off you just introduced.
1. Identify what the follow-up changed
Before responding, name the new constraint mentally. Is the interviewer asking for evidence, an alternative, a downside, a different stakeholder, or a changed assumption? That keeps you from abandoning reasoning that still applies.
2. Preserve what still holds; update what does not
Strong reasoning is stable without being rigid. You should be able to say, in effect, 'Given the new constraint, I would keep X because the evidence still supports it, but I would change Y because the risk profile has changed.'
A follow-up is easier when you treat it as a controlled update to the first answer rather than a second unrelated speech.
Answer the question, then challenge your own answer.
After the first response, ask yourself what assumption you relied on and how the answer changes if that assumption fails.
3. Be precise when you do not know
If a follow-up reaches beyond what you can support, do not manufacture certainty. State what you know, what you would need to verify, and what decision you can still make with the available information.
Practice the second question, not only the first.
Use spoken practice to see whether your reasoning survives challenge, changed assumptions, and requests for deeper evidence.