MiG-31 has engines that are capable of pushing it past it's max speed but it's limited due to canopy material not being able handle friction heat
Those engines are late 60s / early 70s technology, today they could easily make upgraded version (or design brand new ones if they aren't feeling frugal) which could deliver massively superior speed
My understanding is that at flight speeds above mach 3 the rotational speeds of the blades inside the turbojet or turbofan engines is such that they lose their shape and damage the engine beyond repair.
The solution in the SR-71 is to change the flow of air from going through the turbojet engine to bypassing the engine completely.
Those bit pointy nose cones sticking out of the front of each engine can move back and forward... when it is back the air can flow into the jet engine for takeoff and landing, but once it reaches speed and altitude it moves forward so the air can't go into the jet engine... it goes around it... and that bypass air is a ramjet with no moving parts or blades or disks... the only problem is being a ramjet and not a scramjet the fuel has to burn in a subsonic air flow so it would be limited to about mach 5 or 6 at most.
The point is that when the SR-71 is flying at Mach 3.2 there is no air flowing through the jet engines it used to take off with... the air flowing through the engines is bypassing the jet engines and going through tubes effectively operating as a ramjet.
The MiG-41 will likely do the same... if it is designed well and the aircraft can take the heating effect on the various parts of its airframe that will be subject to friction heating, then speeds of mach 4.2 wont require anything exotic like a scramjet.
There are lots of ways they could do it... they might have one jet engine for takeoff and landing and two ramjet engines running down either side so it might be a bit sluggish taking off and landing but at high speed it could be a rocket, or to reduce fuel burn they might have two smaller jet engines to get airborne and for landing and one ramjet for high speed cruise or supercruise at about mach 2 or so.
Ramjets don't need to be big... the scramjet they tested on an SA-5 surface to air missile looked about the size of a large coffee tin on the tip of the missiles nose and drew fuel from the place where the warhead would normally be located... the solid rocket boosters and main rocket motor helped the entire missile to climb to high altitude and about mach 5 flight speed, and then they started up the scramjet which operated for about 90 seconds and accelerated the missile from mach 5 to mach 6 and flew about 180km...
My guess is that they will be making aircraft with standard jet propulsion like MiG-31 only much more advanced and probably larger because it would need to carry it's weapons internally (as for bay size I would go for it being able to fit Kinzhal missile inside or larger)
Side by side seating with pressurized cockpit like Su-34 would also be very desirable
But that's just my guesstimate, we'll have to wait and see
It will be interesting... staying in the same size range will make large weapons difficult to carry internally and this aircraft will need to carry some anti ship and anti satellite weapons that could be very big, though they might be carried conformally perhaps.... they have had interceptors of all sizes and there was even a suggestion that the Blackjack could be used as a large interceptor... the Tu-160P but of course they only made about 30 so it wasn't really a viable option.
Now it is probably not fast enough, but a Tu-22M3M upgrade perhaps with huge AESA and much longer weapon bay...
I am sure they will come up with something cool.
Materials are no longer issues as well, if they have uber awesome materials that can deal with heat from Mach 20-27 on Avangard making some rock bottom variety that handles heat on Mach 4 or even 5 is nowhere near a problem
They might only be able to stand it for a few hours and then need replacing like heat tiles on the space shuttle...
I am not so sure about the engine as explained above, but we will see. Regarding the missiles, why not carrying them recessed? That is way cheaper and lighter, and it will allow the plane to carry very big and heavy weapons. A plane flying that fast and high will be seen from hundreds of km away regardless, I am not sure it makes any sense to give it internal bays either from aero or from detectability point of view. At least not for the bigger weapons.
Of course internal weapons carriage raises the question of can it open its weapon doors at mach 4.2 and release those weapons?
The MiG-31 solves the problem of weapon separation by using weapon hard points with pnuematic rams that throw the missile down when they are launched so they clear the aircraft cleanly before starting their motors even at mach 2.83...
Those patent drawings of missiles stored vertically and fired upwards in flight could be a clue to how weapons could be released... perhaps released backwards, or up and back to start a steep climb to altitude to start their long range flights...
Will be interesting.
This will actually work to it's advantage as it'll be able to launch larger and more capable weapons from within the weapon bays.
Fully internal weapon bays might be problematic... and getting a really big aircraft to fly at mach 4.2 will be harder than getting a smaller aircraft to do the same, though I suppose it doesn't need huge engines for takeoff and landing... once it is airborne if can climb and accelerate and engage a few ramjet engines that would be more than up to the task of getting even a very large aircraft to very high speeds...
Just check out Tu-28 Fiddler, it was huge and was in service for very long time:
It was an interesting aircraft, that was focused more on range than on speed, but both can be important...
Being able to make a Tu-128 faster than MiG-25 while still retain long range and heavy payload will make it rather cool...
The production facilities to produce new Tu-160s means they can make very large aircraft of titanium and other difficult to weld materials and the swing wing box structure needed to have a fast low drag design with the ability to take off and land at lower safer speeds... so it does not need 20km long runways...
The Tu-22M was supposed to be a mach 3 bomber, but fortunately Tupolev managed to make them realise that it would be an enormous waste of fuel and payload capacity and would not be much safer against a modern air defence. For an interceptor however speed has advantages... especially when covering a lot of territory.