Most managers hear this request often, and most of them genuinely want to say yes, but a vague ask puts the entire burden of figuring out what to hand over on them, which is exactly why so many of these conversations end in a noncommittal "let's talk about it" that never quite happens.
The version that actually moves is specific about what you want and honest about why you're ready for it. Naming an actual project, decision area, or type of work, not just "more" in the abstract, gives your manager something concrete to say yes to, or to explain clearly why not yet.
"I feel like I'm ready for more responsibility. Is there anything bigger I could take on?"
"I'd like to take ownership of the vendor relationship, I've been sitting in on those calls for two months and I think I could run them directly. Is that something we could hand off to me next quarter?"
The second version does something the first can't: it gives your manager a concrete yes or no to react to, backed by evidence you're already partway there. Even if the answer is "not yet," the conversation that follows is about a real gap to close, not a vague feeling to sit with.
"I'm ready for more" is a feeling. "I'd like to own X" is a proposal. Only one of them gets a real answer.
Before making the ask, it's worth being honest with yourself about the evidence behind it. "I'm bored" or "I've been here two years" are real feelings, but they're not evidence a manager can act on. "I've handled X well for six months and I think I could extend that to Y" is evidence, it points to a track record, not just a desire.
Timing matters too. Asking during a performance review, when responsibility and compensation are already on the table, tends to land better than asking out of the blue in an unrelated conversation, though a well-timed, specific ask outside of review season is far better than a vague one saved for the "right moment" that never quite arrives. If the answer is no, ask directly what would need to be true for it to become a yes, that turns a disappointing answer into an actual plan.