Yes, this is perfectly acceptable and your new employer does not have to wait until you leave your existing company to commence on the Employment Pass (EP) application. Your current employer will not be aware of the new Employment Pass (EP) application by your new employer.
Your new employer can apply the Employment Pass (EP) for you as soon as they have decided to employ you. The approval may take 4-6 weeks and on receiving the In-Principle Approval (IPA) from the Ministry of Manpower (MOM), you may keep it on standby for up to 4 months before completing the issuance of the new Employment Pass (EP). Thus, it will not have any impact your existing EP.
When your employment with your current company ends and they cancel your Employment Pass (EP), you will officially be given 30-days to remain in Singapore. You can then complete the issuance and pass collection of your new EP card and the process will be completed in 5-7 working days.
Just be sure to follow all the Work Pass application procedures properly and there will be no issue for you.
Find out more information about Employment Pass (EP) applications here.