-p01. 1. Introduction -p04. 2. Preliminaries -p06. 3. Exclusion of multiple flag varieties of infinite type -p06. 3.1. Proof of Proposition 1.2. -p08. 3.2. Proof of Proposition 1.3. -p10. 3.3. Proof of Proposition 1.4. -p11. 3.4. Proof of Proposition 1.5. -p14. 3.5. Case of a=(n), b=$(\beta)$ with $4\le \beta \le n-2$. -p19. 3.6. Proof of Proposition 1.6(ii). -p20. 3.7. Proof of Proposition 1.6(iii). -p21. 4. Triple flag varieties of finite type. -p22. 5. Review of technical results in [M15]. - 5.1 - 5.2 - 5.3 - 5.4 - p29. 6. - p38. 7. - p48. 8. - p54. 9. - p61. 10. - p69. 11. - p76. 12. Appendix - 12.1 - 12.2. - p83. 12.3. - p91. 12.4. - 12.5. - p96. References