As far as I know base on my friend's case in Singapore, if you are a citizen of the other country and you wanted to sue your spouse for commiting adultery/concubinage, If the person who is involve is a Singapore Citizen, you can sue them under Singapore law for commiting adultery/concubinage. But if your wife/husband's lover is another Filipina/Filipino, bring your marriage certificate and approach the Philippine embassy and report them that you intended to sue them ensure you have enough evidence and they may cooperate with you as all Filipinoes has records at the Philippine Embassy and they can easily find them through Ministry of Manpower to the extend they can deport them and continue the case in the Philippines. You have to take action ASAP as Filipinoes are entitled to take Citizenship in Singapore if they have been living there for more than 6 years for those who are not married to Singapore Citizen, and 2 years for those who are married to Singapore Citizen.
If they change their Citizenship to Singapore and did not take dual Citizenship then you cannot sue them under Philippine jurisdiction anymore, as they are already Singapore Citizen and will be protected under Singapore law.
Also bear in mind, technically, there's divorce in Singapore, if your spouse is already a Citizen of Singapore and separated to you for more than 3 years, he will then has right to divorce you
The best thing to do, you are better off to sue him for abandonment and claim for maintenance that will have a good standing in the court.