I think many investors were asking this question on whether multiple applications are allowed for IPOs. The answer is - it depends usually on the size of the issue.
For small IPO issue where they have trouble attracting the 'minimal' 500 or 1,000 shareholders, multiple applications is strictly not allowed. This is because the IPO issue manager is trying to ensure a reasonable spread among investors such that they are able to fulfill the minimum number of shareholders listing requirement.
For big IPO issues such as Global Logistics or Mapletree Industrial Trust, they have no issue or problems attracting and meeting the minimum shareholders requirement. In such IPOs, you can still apply at the ATMs using CPF or Cash even though you are already allocated some shares under the placement tranche. This is because during the book-building exercise, the issue manager already know that they have met all the listing requirements, especially the minimum no. of shareholders requirement.
Hope this answer the query you have. For avoidance of doubt, do consult your remisier or broker but of course, the 'never do homework' ones will not be able to advise you properly. Happy IPO investing.