How do I politely ask for more time without risking to lose the current job offer?

In short, you cannot. The way you are trying to evaluate other opportunities, the organization may also want to evaluate your readiness or commitment to joining. In case you need just a little more time (example: couple of days, as you are on a vacation or some emergency), that is understandable, but trying to stall them for couple of weeks may just off the deal.

If you're currently unemployed, I'd suggest to accept the offer that you have, join them, and then, start looking for better opportunities elsewhere, otherwise you are baking on thin air which may vanish at any time, leaving you with no options at all.

How do I politely ask for more time without risking to lose the current job offer?

In short, you cannot. The way you are trying to evaluate other opportunities, the organization may also want to evaluate your readiness or commitment to joining. In case you need just a little more time (example: couple of days, as you are on a vacation or some emergency) to review the employment conditions and decide on the offer, that is understandable, but trying to stall them for couple of weeks may just set the deal off.

If you're currently unemployed, I'd suggest to accept the offer that you have, join them, and then, start looking for better opportunities elsewhere, otherwise you are banking on thin air which may vanish at any time, leaving you with no options at all.