Most asks don't fail because the answer is no. They fail because they were never really an ask, they were a hint, and the boss didn't notice.
Whether it's a raise, a headcount, a tool, more time on a deadline, or approval to change how something works, the pattern is nearly always the same: the request gets wrapped in so much context and hedging that it stops sounding like a request. "I was thinking, and I don't know if this makes sense, but maybe at some point we could look at possibly adding someone to the team" is not an ask your boss can act on. It's a thought they'll nod at and then forget by the next meeting.
The fix is to lead with the ask itself, stated plainly, and put the context after it, not before. This feels blunt the first few times you do it. It isn't. It's clear, and clear is what actually gets you an answer instead of a maybe.
"So the team's been really stretched lately, and I've noticed some things slipping, and I don't want to make a big deal out of it, but I was wondering if maybe down the line we might think about whether another person could help out at some point."
"I'd like to open a headcount request for one additional engineer on the team. Here's why: we've missed two deadlines in the last quarter because of capacity, not skill. I've attached the workload breakdown. Can we talk this week about whether that's something you can support?"
The second version isn't more aggressive, it's just more useful. It gives your boss exactly what they need to say yes, push back with a real reason, or tell you what would need to be true first. All three of those outcomes are better than the vague nod you get from the buried version, because at least you know where you stand.
A few things worth doing before you make the ask, not after: know the actual number or outcome you want, not a range you're hoping to negotiate up from. Have one piece of evidence ready, a workload breakdown, a missed deadline, a comparable data point, so the ask isn't just a feeling. And decide in advance what you'll say if the answer is no, so a "not right now" doesn't derail the conversation before you've heard the reasoning behind it.
One more thing that changes the outcome more than people expect: timing. Asking for something in the middle of a crisis, right before a big meeting, or in the last five minutes of a 1:1 gets you a distracted answer. Asking with enough runway for your boss to actually think about it gets you a real one.