Last year I read Questions And Answers In School Physics. The book is based on a dialogue between a student and a teacher. A lot of concepts and ideas are seamlessly driven by the dialogue. I found the presentation to be lucid and pedagogical. I am wondering if there is books with a similar style but for mathematics.
Donald Knuth's Surreal Numbers: How two ex-students turned on to pure mathematics and found total happiness is an introduction to Conway's construction of real numbers as positions in certain two-player games. It's very readable and it's written as a series of dialogues between the titular characters.
Lakatos' Proofs and Refutations is a set of dialogues about increasingly general versions of Euler's formula. Most people read it for the philosophy, not the mathematics, but I don't see why one couldn't go the other way.
Also, there are a large number of texts that exposit via pedagogically-motivated exercises, but don't involve multiple interlocutors. I don't know if you consider these to be "generalized dialogues," but if you do, then consider Arnol'd and Alekseev's The Abel Theorem in Problems.
Conics by Keith Kendig is written as a series of dialogues between three characters : Student, Teacher and Philosopher. Student with fresh curiosity, Teacher with an open mind and ability to make connections and Philosopher picking on subtle ideas - these three personalities together develop and explore the content.
There are lots of examples covered and several exercises are given at the end of each chapter.
The series Math Girls by Hiroshi Yuki is both amusing and instructive. We explore together with at first two later three female students some highlights in mathematics like Fermat's last theorem or Gödel's incompleteness theorems.
Currently there are four volumes in this series, the first with this MAA review.
The popular mathematics book Dialogues on Mathematics (original title: Dialoge über Mathematik) by Alfréd Rényi is a set of fictional dialogues about the nature of mathematics between some historical characters (Socrates and Hippocratis in the first chapter, Archimedes and Hieron in the second one, and Torricelli, Niccolini and Galileo in the last chapter).
The book The Square Root of 2: A Dialogue Concerning a Number and a Sequence by David Flannery is, as the title would suggest, written as a dialogue between a teacher and a student. It is quite well done in that it is easy to follow and covers a broad range of mathematical ideas.
This book consists of five acts and two interludes, which are all written as dialogues between three main characters and other supporting characters. Each act discusses the epistemological, institutional and methodological foundations of game theory and economics, while using various stories and examples. A featured aspect of those discussions is that many forms of mutual misunderstanding are involved in social situations as well as in those fields themselves. One Japanese traditional comic story called the Konnyaku Mondo is representative and gives hints of how our thought is constrained by incorrect beliefs. Each dialogue critically examines extant theories and common misunderstanding in game theory and economics in order to find possible future developments of those fields.
I don't think if it suits the needs, but Logicomix by Apostolos Doxiadis and Christos Papadimitriou seems to me to be a great comics book dealing about the history and some concepts of Logic.