If I'm holding with one brokerage and I want to open an account with another and buy more of the same stock I'm already holding, is that lawful or illegal?
There are 4 relevant entities you deal with when you buy shares through a broker:
- the company that issued the shares - you deal with them at AGMs etc after buying their shares;
- the share registry - keeps track of who owns which shares;
- the stock exchange - the place where the trades happen, eg ASX; and
- the broker - facilitates the stock exchange trades.
Each company usually has just one share registry, though some might list on more than one stock exchange. Different brokers might cover different sets of stock exchanges, though the more popular stock exchanges are likely to be covered by most brokers servicing that region.
Since you aren’t buying from the broker (they are just assisting with the purchase), it doesn’t make sense that buyers be restricted to just one broker per stock. In Australia, you can use multiple brokers for the same stock if you wish.
(This is not legal or financial advice; please speak with an appropriate professional prior to making any trades.)