There are reporting obligations for short selling and changes in substantial shareholdings (5% or more) but otherwise, I'd say no; I don't know of daily / weekly records for institutional investors (specific to MAY or otherwise) being published.
I'm happy to be corrected but doubt such a report is capable of being produced unless self-reported. Here now be waffle ...
The ASX website appears to offer historical stock trading data (for a fee) but you won't see the actual beneficialparticipants in the data.
Orders are placed by brokers (the licensed 'market participants') on behalf of their clients. This will include the obvious information, such as ASX code, buy/sell, price, volume, and possibly some kind of order type (price limits and time constraints etc). Behind the scenes, the broker's code will be assigned to the order, as will a unique identifier/s that will be echoed back in trade data and assist the broker in matching an execution to a client. Thus, at no time is the beneficial participant (the client) shown in either order or trade data.
There are some market surveillance tools out there (NASDAQ has one, presumably for ASX Trade) that ASX and ASIC can use to when performing their respective responsibilities as market regulators (including investigations of market misconduct). But I'm guessing they will have to make a formal request for the trade data from the relevant brokers if they need to identify anyone.
I'm older these days and things change, and perhaps have never been... but that's how I recall this little bit of the market hangs together.
MAY Price at posting:
10.0¢ Sentiment: Hold Disclosure: Held
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