The Best Train Ticket/Pass for Multi-Country over 1 week

Are you entirely committed to this trip? You have almost no time in any of these cities.

Look at Rome2rio for a basic introduction. You are not going to spend much money, but the issue is time. 4 cities in 6 days is very fast.

https://www.rome2rio.com/map/Brussels/Stuttgart/Munich/Pilsen/Prague

Brussels to Stuttgart - 4 1/4 hours
Stuttgart to Munich - 2 1/4 hours
Munich to Pilsen - 4 hours
Pilsen to Prague - 1 1/4 hours

In addition, I would imagine that at least one of these trips between cities would be overnight.

Nah, these towns are too close together to have night trains. And they hardly cost a fortune.
Brussels to Stuttgart, 39.90 EUR Sparpreis. Nonrefundable ticket bought a couple months in advance.
Stuttgart to Munich, 17.90 EUR Sparpreis. Nonrefundable ticket bought a couple months in advance.
Munich to Pilsen, 40 EUR Prag Spezial 1-way. Nonrefundable ticket.
Pilsen to Prague, 125 CZK (about $5.50 US)

Even buying train tickets day-of (full fare) won't be "a fortune"

Not only does the Man in Seat 61 know where trains go, he often has suggestions how to save money.

www.seat61.com

I haven't purchased a railpass this century. My experience is all but the longest journeys are cheaper buying point to point passes. It still may be good with a student or senior discount.

If you are planning to make multiple intermediate stops in a day, I've had good luck with day passes in Germany. I doubt, however, they include Brussels or Prague (my day pass did include Salzburg as the last "German" stop).

Thank you to everyone that offered advice. I haven't fully solidified my itinerary, and so the stops/# stops could change. I've also made some incorrect assumptions or not fully investigated everything, and appreciate the education. Keep on traveling!

OK, good. Glad you are not fixed into this. Before you commit, I suggest you decide what you are going to do in each city. Most people would be doing 3-4 things in each one. A simple rule-of-thumb: one activity in the morning, one in the afternoon, travel days lose 1/2 day. Given your 6 days, you have effectively 4 days of actual sightseeing, and you need to remember that 1st and last days are often shortened. You perhaps have 3 actual days of seeing things.

Is that your plan?

What about cutting out Pilsen, or staying in Munich?

FYI, a German Rail Pass could work for a similar trip, but not for your original plan. That is, the German pass covers DB-operated IC or ICE trains (not Thalys) departing from Brussels and also covers DB-operated buses that run directly between Germany and Prague, but does not cover any trains within the Czech Republic. If you end up cutting Pilsen and taking the Munich-Prague bus, then that could be 3 travel days within in one month on a German pass, costing about $227 for an adult, or less if you're under 28 or traveling with a partner.

Seat assignments are not required for the trains on your routes but are required if you opt for that Munich-Prague bus. Reservations cost roughly €4 each in addition to a pass.

The only rail pass that would cover all four legs of your original plan is the Eurail Global Pass for 4 travel days in a month, at $277 for an adult (again less if under age 28). [Edit: If you chose this pass and then also chose a Thalys-brand train departing Brussels, those require more expensive paid reservations with a pass.]

If you decide against a pass, then the most relevant train to book ahead for an advance discount is your first, longest, most expensive one from Brussels to Stuttgart.