Add ½ fluid ounce of Italian vermouth. Garnish with a lemon twist or an orange peel.
Switch the gin to vodka and increase to 2½ fluid ounces. Only use enough vermouth to wet the ice (pour ¼ fluid ounce over the ice and dump out the excess). Skip the bitters entirely. Shake with ice and double strain into a frozen cocktail glass. Garnish with a lemon twist or preferably an odd number of olives.
Reduce the gin to 1½ fluid ounces and add ½ fluid ounce of vodka. Instead of orange bitters and French vermouth, use ¼ fluid ounce (1½ teaspoons) of a Kina Lillet substitute. Garnish with a lemon peel.
This cocktail is not a riff on the Martini, it’s actually the missing link leading up to it. Instead of London dry, use Old Tom gin and reduce to 1 fluid ounce. Instead of French vermouth, use Italian, and up the amount to 2 fluid ounces. Replace the orange bitters with a Boker’s bitters substitute and add 1 teaspoon of maraschino liqueur. Garnish with a lemon twist or peel.
Martini ratios are personal and I prefer to start at a 4∶1 ratio, however this is really up to the drinker to determine by personal preference.