Não há como obter uma reação genérica adicional que possa ser usada para qualquer coisa que exija uma reação. No entanto, existem dois métodos, ambos em Arcanos Desenterrados, para receber mais de uma reação, de um tipo específico, em uma rodada. Túnel lutador, do Underdark Unearthed Arcana :
Tunnel Fighter
You excel at defending narrow passages, doorways, and other tight spaces. As a bonus action, you can enter a defensive stance that lasts until the start of your next turn. While in your defensive stance, you can make opportunity attacks without using your reaction, and you can use your reaction to make a melee attack against a creature that moves more than 5 feet while within your reach.
E o Knight, do Arcanos Desenterrados do Lutador :
If a target marked by you is within 5 feet of you on its turn and it moves at least 1 foot or makes an attack that suffers disadvantage from this feature, you can make one melee weapon attack against it using your reaction. This attack roll has advantage, and if it hits, the attack’s weapon deals extra damage to the target equal to your fighter level. You can make this special attack even if you have already expended your reaction this round, but not if you have already used your reaction this turn.