No — third and fourth holds don't meaningfully exist in practice. Quick context if you're new to the terminology: a first hold is exclusive to one client, and a second hold means you're next in line behind them. Beyond that, in real-world freelance booking, there are effectively only two tiers that matter: first hold, and everyone else, who all get treated as second hold.
Why the ladder stops at two
A second hold already tells a client exactly where they stand: they're not first, but they can challenge for the dates if it matters enough to them. Ranking clients further — third, fourth, and so on — doesn't add useful information, and it actively costs you something: telling a client they're third hold is close to telling them they'll never get the booking. It signals they have no real path to those dates, which tends to just kill the relationship instead of keeping them warm.
Picture five studios all interested in the same week. If you tell the first one "first hold" and the next four "second hold," every one of those four still has a real, equal shot at challenging for the dates. If instead you rank them first through fifth, studios three, four, and five have essentially been told not to bother — and the honest version of that message would just be "no," which is a worse outcome for the relationship than a second hold that's genuinely still in play.
What most freelancers actually do
The common practice is simple: keep first hold for one entity at a time, and give everyone else who's interested a second hold. Every second-hold client has an equal, real shot at challenging for the dates — you're not pre-ranking them against each other.
This keeps the system honest and easy to manage. You're tracking one exclusive relationship (the first hold) and a pool of equally-positioned second holds, rather than an elaborate ranking that mostly just serves to disappoint people further down the list.
It's also exactly the two-tier system Firsthold's Booking Calendar is built around — first hold and second hold, nothing more complicated to track or maintain.
If you're weighing whether to hold yourself as first hold to force clarity among a crowded pool of second holds, that's a deliberate strategy worth knowing about.