Multiple job offers

I have got a job offer which I have accepted but I feel that I was lowballed. My visa is in progress post which I will put down my resignation in my current country and then serve a 60 days notice period with my current employer.
Should I look for other job offers if I find a better job role?
What implications can it have on my visa process?
Also how is it considered culturally to look for other jobs even after accepting one job offer in singapore?