Is it possible to write a redox reaction with two oxidations and one reduction together?

Let's take the Redox reaction between ${MnO_4}^-, {C_2O_4}^{2-}$ and ${SO_3}^{2-}$

Is it possible to write the complete reaction as below or do I need to consider the two reactions separately?

$\ce{4MnO4- + 5C2O4^{2-} + 5SO3^{2-} -> 4Mn^2+ + 10CO2 + 5SO4^{2-}}$

I wouldn't try to combine these reactions. You would want to consider both reactions and maybe look up the standard reduction potentials of all reactants and products involved to give yourself an idea of what is oxidizing what and what is reducing what. In general, you should let the SRP's be a guide for trying to figure out what actually happens in these reactions.

The reaction you wrote doesn't really describe anything chemically. We have to make sure not only the math works out, but also the chemistry. Also, your charge balance is wrong, so even if the chemistry did work out, the reaction would be impossible. You seem to have 24 (-) on the reactants side and net 2 (+) on the products side.

Remember to always check BOTH your mass (MB) and charge balance (CB) work out when you're doing REDOX problems.

The following two reactions are the acidic balanced REDOX reactions for the the species you have written. Of course, these may not actually be the real reactions that would occur. For that, you would have to look things up in tables in your book.

$\ce{6 H+ + 2MnO4- + 5SO3^2- -> 5SO4^2- + 2Mn^2+ + 3H2O} \quad\text{(CB: -6 : -6)}$

$\ce{16 H+ + 2 MnO4- + 5C2O4^2- -> 10 CO2 + 2Mn^2+ + 8 H2O} \quad\text{(CB +4 : +4)}$

With two species being oxidized the overall reaction is complex. Given some starting concentrations it is unlikely (more like impossible...) that both reactions proceed at some constant relative rate. So the net overall reaction would depend on what the absolute and relative concentrations of the two species being oxidized. So trying to think of one overall reaction is almost certainly likely to lead to problems.