Is it possible to have an asset that may receive two different partitions? For example, I want to run the asset daily using a daily partition, but I would like to use the same asset on monthly partitions for backfill. Is it possible to achieve?

Not quite sure on exactly the details here, but you can have an asset handle a range of partitions. You can also have offset partition relations and such. May be worth checking out the latest community video. Sandy went over a lot of features in it, it's quite good!