@DaniëlT I thank you for your interest in this project, and I believe your interest is sincere. This is a DIR, but I'll answer you once.
I haven't thought out to the full what form this Dharmic unity ought to take, but I suggest a more specific kind of ecumenical-style dialogue- like a council or panel. This dialogue would be more specific because the Dharmic religions share more in common than we disagree on.
Having looked at all three of them- I personally think we argue about details 9 times out of 10 in any given case, and not per se actual irreconcilable differences. What I'm saying is the differences that are there can be worked with. They aren't so great that this project couldn't happen out of a shared concern for living things.
Buddhism and Jainism are schools of Indian philosophy, just as the Hindu orthodox schools are. This means we share a similar core at the heart of our ideologies present in most all Indian schools to a degree. We're concerned with why dualism presents itself to the mind and what it actually means, as an example.
Is dualism a real appearance in the world? Is it only a seeming appearance?
These questions come before any categorization of orthodox and heterodox among Indian traditions of belief and thought. Our main difference as Buddhists and Jains is our rejection of the Vedas, but in most ways- our basic premises and the questions we're setting out to answer are not different.
No doubt, some may feel I've been too general. That's okay though. I don't hold their personal opinion against them.
@Aupmanyav already said what the purpose of such a unity would be. There's more to all three religions than the reality of Dukkha, but we're all very concerned with it. It's a shared concern.
Ahimsa is a value shared by many Hindus, together with Buddhists and Jains. Ahimsa is the active dimension of the desire to tackle Dukkha as a problem. When one begins to carry that desire into action as ethics and a lifestyle.
That would be one great benefit. We'd be a more unified force in tackling suffering, which is more effective in a present world where numbers still somewhat matter.
However, it would also be continuing a tradition that has persisted for centuries between Hindus, Buddhists, and Jains: discussion of our seeming differences, which has greatly enriched all three traditions over time.
We relate to one another enough as traditions of Indian thought- that our arguments can be mutually beneficial. We can accept common insights and grow.
I hope I haven't violated DIR guidelines. I did it with good intent.