You can hire all the people you want into a sole proprietorship.
You should read the two threads below because they contain real life information of people who tried to start up a pte ltd and failed.
http://forum.singaporeexpats.com/viewtopic.php?t=75000
http://forum.singaporeexpats.com/viewtopic.php?t=60398
The actual process is straightforward.
a) Form a Pte Ltd with ACRA.
b) Transfer all assets of the SP to the Pte Ltd in the form of paid up capital.
c) Change all your bank accounts, trade accounts, and leases.
d) Close your SP.
If you've read the threads above, you'll understand that because you are a DP on LOC, you have additional hurdles to jump over.
a) You will need a resident director to handle all the paperwork since you, as a DP, cannot legally work for a Singapore entity, and being a director is work in the eyes of the gahmen.
b) Realistically, you will want to be working on an EP for your Pte Ltd, so that you can become director and have full control over your company. Are you earning enough to qualify for an EP?
c) Have you got a solid business in place and a solid business plan?
Bottom line: If you have a viable business, experience, cash, and a plan, chances are reasonable to good that you will be able to get your EP and become a director of your Pte Ltd.
But, if you do not do your homework, you will fail. For example, buried in the threads is the story of a fellow who planned on paying himself X dollars but failed because he didn't demonstrate enough revenue to cover the salary. Or, the fellow who was told to that foreigners could only work under an Entrepass.
Neither of these are entirely correct, and they do demonstrate the importance of convincing MoM that you are a competent business person and that you have a viable business entity.