The mashup innovation ideation technic goes even further with the constraints. Yeah it's possible.

In a first round, participants have to list problem areas. Here people list for example frustrations people have in the situation today or list needs that people have expressed.

In the second round, participants list solutions areas.
Here people list for examples available internal and external resources, tools, technologies, partners, services. 

These constraints can also be gathered before by the facilitator.

In the third round of the exercice people get assigned in group or solo one  random element from the problem area and one random element of the solution area.

From there, people have to create one or several ideas based on these two constraints.

You can then repeat the exercice by selecting new random problems and solutions. 

I've personally used this ideation method when I was working with a car manufacturer where we wanted to create new services but based with what the manufacturer already had. So the engineering team made a list of all the available data the car could give us. Then every team received randomly two data sources and had to create with it a new service that would make the driving experience more fun, secure or interesting. 

Here we just used solutions elements and kept the problem areas open. 

This example shows that as with every technic from the innovation or design world, feel free to adapt the  tool to your context.