Introduced by our friend enigma, cov3r is a small change to the rules
which makes a big change to the game.
The only new rule, which applies to all colors, is this:
In addition to your first move covering the corresponding
corner square, it must also cover the two adjacent squares,
the three of them being in a V3 configuration.
Hence the name coV3r!
(See Fig 1, left).
This limits your choice of initial pieces for each color
to those shown on the right in the adjacent diagram.
(The colors here are not significant - any color can choose
any of the seven pieces for a first move, as long as it
covers the "corner-V3" squares.)
A possible coV3r start is shown here (Fig 2).
The result is more open game, balanced between blue/red and yellow/green, because the 4th blue cannot connect with the 3rd red, disabling the so-called "power openings", or "wall games".
Give it a try and see if it doesn't lead you to more variety, and a real change of pace for the game.