How to ask for more time before starting a new job

I have got a good job offer but I have already delayed my start date by a couple of weeks.

But my current company needs me for another 1.5 more months. This is after the notice period so it's just to help them transition to someone else - i.e. not contractual but on good will. Is there any chance that I can ask for more time with the new company for that much more time? How do I explain this?

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