Resolution goes by the capabilities of the monitor and game and cant increase resolution past the monitor's limit. For example there are 1080p, 1440p as you said and 4k monitors available for purchase. Depending on the optimal resolution capabilities of the monitor will also depend on the game and if it also has the resolution to fit natively. Modern games have support for high resolutions as that's whats current. Older games with no high resolution support in the UI can sometimes be edited manually in a config or ini file if your lucky or there may be an HD pack available.
Searching an old game and resolution you want can sometimes find related discussions. ie Doom 1 4k for example can lead you to mods that can take original Doom to...