You can ask. Firms know candidates may be managing overlapping processes, although they are not obligated to extend the deadline.
Be specific about the date you are requesting and explain the reason without oversharing. A concrete request is easier to evaluate than 'I need more time.'
Do not assume you need several additional weeks. Ask for the minimum time that actually resolves the conflict, and be prepared for the answer to be no.
If the extension is denied, make the decision based on the offer you have and the value of the unfinished option rather than waiting indefinitely for perfect information.