Martijn Aa This design could be conveniently analyzed by using path analysis, which is available in software programs for structural equation modeling (SEM) such as lavaan (in R; free software), Mplus, AMOS, LISREL, EQS, OpenMx, etc.

Path analysis allows you to consider multiple IVs, DVs, and mediators in a single statistical model. It also allows you to conveniently test the indirect (mediated) variable effects for statistical significance. Many SEM programs have specific features for automatically printing and testing indirect effects (e.g., by using bootstrap confidence intervals as provided by, e.g., Mplus).

Christian Geiser has given you good advice about how to estimate your model. I will follow up by suggesting that you study the following articles carefully before attempting to interpret any indirect effects you might find. HTH.

MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding and suppression effect. Prevention science, 1(4), 173-181.

Fiedler, K., Harris, C., & Schott, M. (2018). Unwarranted inferences from statistical mediation tests–An analysis of articles published in 2015. Journal of Experimental Social Psychology, 75, 95-102.

Christian Geiser Thank you! Is there also an option to do a path analysis with multiple IV's and DV's using SPSS? Or how should I do this in SPSS?

Unfortunately, SPSS does not allow you to run path analysis, at least not in a convenient way. Some types of path models can be run as sequential multiple regression analyses (which allow you to estimate the path coefficients as regression slope coefficients). However, this is tedious, and it only works for "just identified" (saturated) path models.

To use path analysis effectively and efficiently, I'd recommend that you use a specialized program for SEM. I mentioned the most commonly used ones in my initial post above. Note that lavaan and OpenMx are free. AMOS is commercial but user-friendly as it allows you to specify a path analysis by drawing a path diagram. Mplus and EQS (also commercial) and other programs have similar options that make it easier for beginners to specify a model because you can generate the syntax/code from a path diagram.

When considering SEM vs mediation via process this paper may help:

Hayes, A. F., Montoya, A. K., & Rockwood, N. J. (2017). The analysis of mechanisms and their contingencies: PROCESS versus structural equation modeling. Australasian Marketing Journal, 25(1), 76-81.