PostgreSQL multiple transactions on the same connection

If with unrelated you mean one after the other, then the answer is yes.

If you mean having different transactions open at the same time, then the answer is no (there are some hacks available using dblink but I don't think they qualify as "on the same connection).

If you mean "interleaved transactions" as required by the Java JTA standard: No, there is no support for that. See this JDBC FAQ section for this and why it is not a big loss.

Also the PostgreSQL core does not support something like this.