Am I restricted to buying stocks in multipliers of 1000?

The lot size has already changed to 100 min shares on the mainboard SGX.
There is still the odd lots market that caters to those who want to trade in odd lots less that 100 shares.

It wil largely depends on the market and company you invest into.

For Example, in US Market, it is trasacted in 1 unit, i.e. 1 lot = 1 unit.

For Taiwan Market, their stock are mainly traded in 1000 multiple.

For Japan and Hong Kong wise, it varies, it may be 1000, 2000, 100. So depends on the company it self.

For Malaysia and Singapore, it is in multiple of 100.