That works, but they are more likely to pass something with exceptions than without. So sometimes you have to do what you can and fight again another day.
Yes, the Hyde Amendment couldn’t be passed without those two exceptions. I was there in 2000 when it was passed for that session, and a young congressman asked the question of why the two exceptions, and Hyde answered that it was the only way to get it passed. Only later did I realize that was probably a set-up question rather than spontaneous, so that it would be on the record.