Center for Reducing Suffering researches ways to best reduce suffering. 

StrongMinds focuses on providing mental health services to women in Africa - particularly treating depression. 

I'm sure there are many others. I'll add them if I think of them. Might be good to have a master list of suffering and/or s-risk focused groups. 

"Invincible Wellbeing is a research organisation whose mission is to promote research targeting the biological substrates of suffering."

Appears on the 80,000 Hours Job Board

In addition to (farmed and wild) animal organizations, OPIS is worth checking out.

Here's a list of organizations focusing on the quality of the long-term future (including the level of suffering), from this post:
 

If you are persuaded by the arguments that the expected value of human expansion is not highly positive or that we should prioritize the quality of the long-term future, promising approaches include research, field-building, and community-building, such as at the Center on Long-Term Risk, Center for Reducing Suffering, Future of Humanity Institute, Global Catastrophic Risk Institute, Legal Priorities Project, and Open Philanthropy, and Sentience Institute, as well as working at other AI safety and EA organizations with an eye towards ensuring that, if we survive, the universe is better for it. Some of this work has substantial room for more funding, and related jobs can be found at these organizations’ websites and on the 80,000 Hours job board.

For community building, there's the International Suffering Abolitionists group. It hosts meetups, a Discord server and a section of EA Gather Town.

Aren't global health charities like SCI and GiveDirectly slam-dunk answers? I switched to donating to them more than the AMF precisely because they seem to rank better as suffering alleviation rather than just saving lives.

As for whether NTD charities are funding constrained, I think obviously yes? GiveWell, as an example, put the SCI's room for more funding at a whopping $85 million last year. By contrast consider how everyone's favourite anti-malarial charity AMF has a funding gap of around $33 million. So in my head the SCI clearly has huge capacity to alleviate a ton of horrific suffering... They just lack the funds. This also isn't even considering all the other deworming charities. Last I checked the SCI has the most room for more funding out of all of the GiveWell recommended deworming charities (when deworming was still recommended that is) which is why I aggressively donate to the SCI.