Constraintless conceptual model of organization with constraints?

We've been given an assignment in which we are to create a conceptual model, described by a text document. There are a number of constraints given in the document, but we have also been instructed not to use constraints in the model.

We have been able to work around a few constraints, but there is one that we've been unable to tackle. I've made up a scenario that is somewhat similar to the part of the assignment that we're having issues with.

You've been tasked to create a model of the structure of a game studio. The company consists of a number of departments, and each department has at least one employee. Each employee works at a single department. There are three different types of employees: developers, designers and engineers.

In addition to this, there are a number of leadership roles that employees can have: Head of Department, Deputy Head of Department, CTO or CEO (Yes, CTO and CEO are roles that regular employees have). Each department must have 1 Head of Department and at least one Deputy Head of Department.

In addition to this, there can only be one CTO and one CEO, and these roles can only be held by engineers. Each employee can only have a single leadership role.

To solve this, we've made up an additional, abstract entity: BasicRole. This entity is a specialisation of LeadershipRole, and is a generalisation of the three roles that any employee can hold. That solves one of the problems, and now we can simply create appropriate associations between Designer/Developer and BasicRole

However, we also want Engineer to have an association with BasicRole in addition to associations to CEO and CTO. Adding those associations results in a conceptual model that looks as such:

However, this is problematic because now we're saying that an engineer can have anywhere between 0 and 3 roles.

We've considered including Company as an entity and adding associations between Company and CTO/CEO, to specify that way that the company can only have one of each, but we've been told over and over during this course not to include the thing that we're modeling as an entity in the model.

Now, it seems as if all our problems could be solved with constraints (if we were to go ahead and read up on those), with some sort of xor for the three associations. However, seeing as we've been instructed not to use constraints in the conceptual model, we're at a loss.

If you associate your Engineer to LeadershipRole (with multiplicity 0..1) removing your two relationships from Engineer to CTO, CEO and LowerRole you will get the expected result:

Each employee can only have a single leadership role.

Since LeadershipRole is abstract it has to be either CEO, CTO, HeadOfDepartment or DeputyHOD) but due to the multiplicity can't be more than one at the same time.

The "we've been told over and over during this course not to include the thing that we're modelling as an entity in the model" statement is correct if you're designing the code-level documentation but it is normal to put the entity representing the whole organisation you're modelling. In other words - don't put System (or however you call your system) in your system's model. But Company is something you model within your system.