We actually can; we do it already.
For example, we need oil primarily to make gasoline right now. But if you just use a fractionation tower to get the right light fractions to make gasoline from crude oil, you can only use about 5% of the barrel for gasoline (and naptha, and kerosene, and butane, and the rest of the lighter fractions.)
To increase our production of gasoline, we do something called cracking. We use either thermal or steam cracking to reduce the length of the hydrocarbons in crude oil so that a greater percentage of them can be fractionated out into gasoline. As a result, 45% of a barrel of oil can be used for gasoline, and over 50% can be turned into those lighter fractions.
We adjust this process (pressures, temperatures, dwell times) to produce a feedstock with the fractions we want. We can adjust this in either direction, to get more heavy fuels/products (bunker fuel, asphalt) or more lighter fractions.