In its current form, no-- but the content collaboration and task management you're describing seem reasonably straightforward to implement.
Courses as they exist now are unaware of semesters or terms, and are only tied to the students enrolled. So if the students enrolled in a particular class don't change (or change very little) between two semesters, you could continue use the same course for a 2nd semester if you wanted, or you could import your students into a new class and name the new class "Class Semester 2" for example.
I'm happy to work on features to fit your use case if you're interested in offering suggestions or are looking for a better solution than your current one; my email is brad [at] gradefinity [dot] com and I'm generally pretty available to talk about features/suggestions/demo stuff, etc.
Gradefinity (https://gradefinity.com) is a kind of Blackboard + Scantron LMS alternative that is really targeted in terms of what problems it intends to solve (in-person and online tests, gradebooks, and communication).
Full disclosure: I built it-- I'm very receptive to feedback and feature suggestions though and am looking for pilot schools if anyone is interested in shaping the platform/knows someone who might be.
Moodle is a popular open source LMS (learning management system) written in PHP that could use a ton of improvement, especially on the front end. It's not necessarily bad, but it is very outdated compared to offerings by private companies.
Courses as they exist now are unaware of semesters or terms, and are only tied to the students enrolled. So if the students enrolled in a particular class don't change (or change very little) between two semesters, you could continue use the same course for a 2nd semester if you wanted, or you could import your students into a new class and name the new class "Class Semester 2" for example.
I'm happy to work on features to fit your use case if you're interested in offering suggestions or are looking for a better solution than your current one; my email is brad [at] gradefinity [dot] com and I'm generally pretty available to talk about features/suggestions/demo stuff, etc.