I know it is possible because I have done it before but for the life of me I cannot remember how. I know there appears a red check in the box to the left of the request once you do it. Going through and individually picking the requests I want to keep takes way too long and I would love to select multiples even though I cannot go on multiple quests a day. Thanks!
Well you can obviously rip off a job request by selecting "no" when Azumarill asks you if you want to set out on the job. Just keep doing this multiple times. (Hope this helps!) :)