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How to buy bonds in the primary market

I know it's generally done at the institutional level, because they're the only ones who could afford the ginormous lots. But what if I managed to collect a comparably large sum of money from a group of people and offered a slightly higher price to the issuers? I'm thinking this, because that would still be cheaper than purchasing the bonds at the markup that the institutions place before placing them on the secondary markets.
Your question is a bit generic and not well defined so I may not give you the answer you might be expecting. But assuming you are referring to plain vanilla corporate bonds, the underwriters (and not just any institution) who are responsible for selling the bonds to the public in the primary market have a large and complicated role including regulations which they have to follow. Their role involves also advising on the type of bonds and coupon for the borrower. So, even if you had all the capital to bid for the whole lot of debt that a bond issuer might desire to issue, I personally do not know how you could do it without going through the "standard" process of the underwriters. I am referring to the US capital markets.