Can I drop the word "like" in certain instances?

The particular example I am thinking of here is: “This sounds like a noble pursuit.” I was wondering if it would be grammatically correct to drop the like: hence, “this sounds a noble pursuit.”

It sounds correct in my head and out loud (much to the confusion of my co-workers) but I don’t think there’s any grammatical precedent. Is it actually correct? If not, are there times when I can drop the ‘like’? What would those times be?