In Belgium the shareholders of a private limited company are not in a public register. The directors are, and in practice that gets you almost everywhere you want to go.
Where to look
The Belgian Official Gazette. Every appointment, every resignation of a director and every change to the articles is published there, with a date. Search the company name and read from old to new: you see at a glance who arrived, who left and when something structural changed.
The Crossroads Bank for Enterprises. Gives the legal form, the incorporation date and the current officeholders.
The annual accounts. The full schedule lists participations: which companies this agency owns, and sometimes who owns it.
IKAg's factsheets. They show per agency which group it belongs to, with an overview by group. That is the level above the agency: the holding or the international network.
What to watch for above all
Recent director changes. Three changes in two years is a signal, however good the work. Ask about it; the answer is usually harmless and occasionally important.
A holding that is not Belgian. Decisions are then taken elsewhere, and you notice that faster in a bad year than in a good one.
A founder who has left the board. At small agencies the founder is often the reason the agency is what it is. Their departure is not a detail.
What you can simply ask
"Who are the shareholders, and has anything changed in the past two years?" is a normal question from a client considering a three-year contract. An agency that gets uncomfortable has a reason, and you want to know that reason.
See also: which group an agency belongs to, network or independent agency and does this agency still exist.