No, as a general rule you cannot stack identical effects on a creature
The DMG explains this in chapter 8, "Running the Game", under the heading Combining Game Effects:
Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items.
A creature who is already affected by your Martial Discipline: Weretouched class feature can have the effect applied to them a second time, but they will still only take the 1d4 of damage each round. However, if the second application's duration will outlast the first, at the point the first application wears off, the second will still be in effect, and so the creature will continue taking damage.
As a note, this feature needs some editing to remove a bit of ambiguity and dubious parsing; one suspects that it is meant that the effect ends if someone uses an action to apply one use of a healer's kit to the creature, rather than just when anyone anywhere happens to use a healer's kit, and that the alternative option of making a medicine check should also be done as an action.