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Why can't we have n-levels of cache ?
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Generally cache is used to "reduce the access time"

if you n-level cache, then if cache$_1$ miss, cache$_2$ miss, cache$_3$ miss, ......

then unnecessarily you increase the average access time. ( note you have to think it is sequential access. )
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Practically speaking computer architecture people will add more levels of cache only if you prove it can bring a performance benefit. If you can do it then we can have 5 or more levels of cache too. As of now 3 is the standard. In future if memory speed changes we can have more but very unlikely.
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sir, on one of the gate question comment, i read that,

" We are using Simultaneous approach in practical. " --- how this can be true ?

then we should have, complex hardware structure, right ?

let if i can pay more cost for hardware then it can be implemented for n-level cache ?
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Simultaneous is practical for lower levels of cache. It is not about just money, but practical speed issues. If one tries to implement simultaneous access for L1, effective access speed will be lower.

Same for n level, not just money but you have to prove that there will be performance advantage. If possible adding more memory to higher level is beneficial than adding a new level.
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thank you sir!
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Sir, how do we measure performances for different caches? e.g 3 level and 5 level cache?