Prayer Question

I've begun offering up my sufferings for the holy souls in purgatory. My question is, is it possible to offer up your sufferings for something like (all of the children who are being bullied and abused) or (the homeless) or so forth. Or even speffic people could i offer up my sufferings for a friend that is not living a holy life so that god will have mercy on them? I feel like it would be helpful to other souls to offer up my sufferings for things like this but ive never heard of it being done and dont know if its okay. Thanks.