1.) I know the consensus here seems to be to publish in different journals, I will just give a famous example for the mix in which the series of articles were all published in the same journal. Not only that, but Part II and Part III were even published in the same issue of that journal.
J Cheeger and T Colding (1997) On the structure of spaces with Ricci curvature bounded below I. J. Diff. Geom., 45: 406-480.
J Cheeger and T Colding (2000) On the structure of spaces with Ricci curvature bounded below II. J. Diff. Geom., 54: 13-35.
J Cheeger and T Colding (2000) On the structure of spaces with Ricci curvature bounded below III. J. Diff. Geom., 54: 37-74.
2.) Another example in theoretical physics is given by the series of two papers by Dine, Seiberg, Wen and Witten on nonperturbative effects on the string world sheet. The two papers were originally published in the same journal: Part I and Part II.
3.) Sturm published Part I and Part II of his two-part series of articles on the geometry of metric measure spaces in the same issue of the same journal.
4.) Yet another example on the engineering side, I just saw a series of two papers on waves and turbulence modelling, both published in the same journal: Part I - Formulation and Part II - Applications.
5.) Famous example from topology:
Hopf H., ''Abbildungsklassen $n$-dimensionaler Mannigfaltigkeiten'', Math. Annalen 96 (1926), 209-224.
Hopf H., ''Vektorfelder in $n$-dimensionalen Mannigfaltigkeiten'', Math/ Annalen 96 (1926), 225-250.
So it hardly seems unusual to publish a series of papers in the same journal, even when the final article in the series is different to the others and focussed on applications.