I assume that the output terminal of which you speak is not merely a DC power supply. I assume that it serves a control function, in addition to powering something.
If so, then it's hard to say what the effect of bulking up to 440 μF might be. At least two modes of failure are possible:
- The output signal at 440 μF might be unusably sluggish. The printer thus might not respond. Reducing the capacitance to 200 μF or 220 μF again would fix this problem.
- The 440 μF might draw too much current at the output, storing too much energy too fast. This would not harm the capacitor but it might render the board permanently useless.
Fortunately, #2 is unlikely. Even #1 is fairly unlikely.
Let's talk about #1. The output has an output resistance Rout, and the lower, the better; but for this kind of electronics, unfortunately, it's probably fairly high. The off-board load—that is, whatever it is that the output drives—will have a variable impedance, which means that it draws a variable current, which is why you have a capacitor tapped to a point between: the capacitor supplies the variable current so that the board's other electronics do not have to. The bigger the capacitor, the better it can supply the variable current, so that's good. Regrettably, the bigger the capacitor, the longer the period the output shall want to switch from low to high or high to low.
Switching is not instantaneous. The larger the capacitance, the slower the switch.
The time needed to switch will be approximately t = [-ln(Vmargin/VCC)][Rout][C], where probably 1.0 < -ln (Vmargin/VCC) < 1.5 and where C is your capacitance.
Regarding scenario #2, the potential problem there is that the board's electronics supplying the output must generate switching heat in proportion to the capacitance C. The heating rate dQ/dt will not change, but because the time t is longer, extra heat will be generated each time the output switches low to high or high to low.
Fortunately, outputs like these tend to be designed to handle a lot of switching. Even more fortunate (if you wish to call it fortune) is that #1 limits the effective switching rate. So #1 counteracts #2 to a significant degree.
I hope that some of that makes sense. If you wish to make some extremely rough calculations, then you might assume that Rout = 1.0 kilohm. (For better calculations, construct a voltage divider to measure Rout by Thévenin's technique.)
If you want my recommendation, though, I would be inclined to leave the 200 μF alone, unless you just wish to experiment and do not mind the risk. Otherwise, @StainlessSteelRat is right: "Hard to see a manufacturer changing a design without correcting a known problem."
You say that your version of the board has a supposed fix, but isn't it more likely that the supposed fix is just a fix?