Assassin is prestige class from DMG with 10 levels and arcane spells progression. However, it does not progress arcane spells of existing class, but it has its own spell list and spells progression in contrast to some other prestige classes which continue progress on existing arcane casting class (via +1 level of existing arcane spellcasting class), like Unseen Seer.
Unseen Seer from CM also has 10 levels, and on each level progresses existing arcane spellcasting class.
What happens when character is already level 10 Assassin and takes level in Unseen Seer (or other prestige class that continues spell progress in such way)?
There is not Assassin's spells progression beyond level 10.
For level 10 Assassin, do levels of prestige classes, which advance spells progression, only increase character's caster level?