With my second book, when the first in series was self published? It was received really well, and currently has 4.5 on amazon. Would the publisher be interested in a second in series, without the first?would they consider taking the first after it had already been self published? My problem is the second book cannot really be taken as a stand alone. I'm asking this well in advance of the story being anywhere near ready, purely because I want to give a publisher a try with this one. I never thought the first would be good enough to sell but its exceeded my wildest expectations. if I need to alter how I approach this story line in order for the publisher to take it id rather do it now than just before i press the publish button. The only reason its not 5 stars is the marketing/cover/blurb etc isnt my strong point, and however hard I tried there are a couple of spelling mistakes still present.
I've talked to some agents and publishers about this issue. The answer to both appears to be 'it depends.' There are publishers who have taken on self-published works. I don't know of examples offhand of any who bought a second in series only, but it is possible that there are some. They're not going to care about the 4.5 rating, in my view. They're going to care how much you've sold and about whether they think they can market the work itself.
You don't. Most publishers won't talk to you at all without having an agent and I'm sure your agent will tell you that your second book is dead in the water as far as traditional publishing is concerned, at least if your first book didn't sell like hotcakes. And that means 50k+ demonstrably sold.
I don't have an avatar of a feline covering it's eyes, but... Like others said, you don't. You need an agent. It's the only way in the door if the work is unsolicited. And an agent likely won't want to jump into the middle of a series, especially one with bad cover art and typos (by your admission). Ratings don't matter, only sales. Fifty shades of grey was self-published. It had low ratings but phenomenal sales, so the publishers approached her realizing the potential if they backed it with a marketing campaign. Also, if it looks like you haven't invested in your own work enough to get proper cover art done by an artist, or get a proofreader, they won't be all that interested in putting in their money to do it for you. Self-pub will only lead to deals if your sales are irresistibly good, or the publisher falls in love with your work when they find it for themselves. Publishers and agents do still love books, and book deals are sometimes struck not for money but the industry folk being big fans. It's rare though.
Maybe consider focusing on doing very well with this (current) series (first few books) and then, with the first book in another series (or possibly a standalone novel), seek representation from an agent or to directly submit to the publisher (slush pile)--it depends on the genre, and even the size of the publisher as to whether they accept unsolicited manuscripts.