Is there a term for an algebraic structure with two binary operators that are closed under a set? For example, let's say we're using the operators +, and *, and the set {0,1,2}
The Cayley tables look like this:
* 0 1 2    + 0 1 2
0 0 0 1    0 1 2 0
1 1 2 1    1 0 1 0
2 0 0 2    2 1 2 2

These Cayley tables are totally random, but the point is that the algebraic structure isn't necessarily like any other common type of algebraic structure with two binary operators (e.a. field, ring, boolean algebra). The two operators just obey closure, so it's basically an abstraction of a magma to more than one operator.
Is there a specific, agreed upon name for this in mathematics yet? The most obvious thing to me would be to call this a bimagma, then to call something similar with three binary operators a trimagma, then in general a n-magma. Do these structures have a common, agreed upon name?

From Burris, Sankappanavar A Course in Universal Algebra page 26 (42 of the pdf): "An algebra A is unary if all of its operations are unary, and it is mono-unary if it has just one unary operation."
Although from what I read it is not clear whether or not in practice this terminology has been extended before, an algebra with two binary operators could be called di-binary.
