Per the OP's request to make this a basic engineering study on what would be possible, I will keep my future comments on what is possible to build, not on what designs they DID build in canon. I will start by copying the most recent relevant post on the matter since it makes most of my arguments for me and I'd rather not retype everything. ;)
In answer to the question of WHY the TC would build an MBT, the TC would build a new MBT because in the 3020s...and the 3030s...and the 3040s...and the 3050s...(ahem), the TDF was being bolstered by constant spending at the orders of the Mad King Tommy so it would be ready to repel the inevitable Davion invasion. For this, they would need an MBT, something with big guns that could stop an invasion cold if produced in sufficient numbers.
The 60 ton Manticores MIGHT fit this bill, but they lack short range "get out of here or die" punch. For that, the two upper class autocannons are much better. Of course, there will always be room for a Manticore's particle cannon in any well rounded army. ;)
Now based on canon, the Taurians really hardly use any tank above 70 tons. Anything larger than that is very rare. So if we are looking at a new design for the Taurians to build to stop the inevitable Davion invasion cold, it is going to be somewhere in the range of 60 to 70 tons. Better or equal to the Manticore, cheap to build, good mobility, good firepower. Built by the lance, they can kill allot of stuff. :)
Beyond that, a good MBT needs to keep up with the main battleline, suggesting a minimum speed of 4-6 based on the speed of the basic Taurian trooper (Thunderbolt) and "assault" heavy BattleMechs like the Warhammer.
Based on all of that, the most wished design would be in the 60 to 70 ton range, move 4-6 or maybe 5-8, and have a PPC, AC10, or AC20 as its main weapon. Extra room would go to filler weapons like machine guns or missiles.
The reason I pick those three weapons as main MBT weapons is because they are the only three weapons up until the 3050s that the TC has ready access to that do 10 or more points of concentrated damage. We can live with something that does 5 points on a skirmisher or an LBT like the Vedette, but for a true MBT of an interstellar nation you NEED heavier concentrated damage. And those are the only three weapons that really fit that bill.
So that covers the weapons that you would want on an MBT. What about the engines? Well, if you are thinking ICE, honestly you just say they build it. It's literally not rocket science to build an ICE engine and anybody can do it. ;) If you are thinking a fusion powered vehicle, things get more interesting. In 3055, the Taurian Concordat builds four engines that can conceivably fit in a 60, 65, or 70 ton chassis. The 180 and 300 give a 60 tonner the ability to move 3-5 or 5-8. A 5-8 60 tonner could be all kinds of cool. :) There is no 240 engine in 3055 that could make it move 4-6. The TC also builds 260 and 280 engines that can make 65 and 70 ton vehicles move 4-6.
Whether or not they COULD build the 240 engine is going to depend on a number of issues. They build engines a little bit weaker and a little bit more powerful, so they COULD tweak one of those. But until the 3050s, the fusion engines are really going to be complicated enough that tweaking one is NOT going to be fun. Until the 3050s, I'm not going to consider that a possibility unless someone can find a canon source that says they did something like this. So let us go onto the question of whether they built the Manticore at Perdition before they started building the "Not a Rommel" there. As fusion capable factories do not get built out of nothing in the 3020s, it would make sense that they would have built another fusion-powered MBT there, and of any fusion powered MBT in the universe in the 3020s, the Manticore is the one that would be most likely for them to build due to their pseudo alliance at the time with the Magistracy. This is of course supposition though, and IF they built them in the past, they stopped building the 240 by the 3050s since there was no use for it. Of course, by the 3050s, the TC and Magistracy were involved in a TRUE alliance, and they were building new fusion-capable factories, so in the 3050s it would be easily acceptable and in tune with their capabilities for them to build a NEW line of 240 fusion engines then.
Having said all of that, my basic engineering proposal concerning what they would want goes to the following ideas:
Tonnage: 60, 65, or 70.
Speed: 3-5 (too slow really, but it brings interesting enough possibilities the TC would not throw such a design out without looking at other abilities), 4-6, or 5-8.
Main Gun: PPC, AC10, or AC20
Secondary Weapons: Medium Lasers if using fusion engine, Missiles (preferably LRMs for range, but SRMs for street clearing would be interesting), and machine guns.
Any combination of those capabilities would make a very good MBT, except the 3-5 movement. That is really too slow, but if a company brought a design in at that speed that had some REALLY amazing capabilities to make up for that speed, the TC might be willing to gulp the slow speed down and accept it.