The katakana changes with time, and so recently they introduced the "v" "ヴ", and I'd like to know if there's a possibility they'll add letters like "si" "セィ" or something similar in the future? Do the Japanese government has some plans for that or not?
There are no plans that I know of, but I would be surprised if Katakana (and even Hiragana) does not change over time. Writing systems tend to change with time, to better reflect natural changes in the languages they represent. So the real question should probably be whether there will be a change soon.
And maybe there will be change soon, since already some Japanese can perfectly distinguish between
[shi], snd it seems like the Japanese government isn't too conservative about small changes to the gairaigo spelling rules.
Anyway, I'm not sure that there is a definite answer to your question. Unless the Ministry of Education (which is in charge of these things, AFAIK) is working on a solution right now, everything we can say is just speculation.
I'd be surprised if the カタカナ didn't change at all; they changes with 日本語 to better express 日本語. Sounds like スィ and ウィ likely arose due to a need to better express how a borrowed word is pronounced in the original language.
Over time, 日本語 and カタカナ will undoubtedly change to suit possible new sounds and language constructs as people need to express new things. I agree with Yaniv; it isn't a question of whether it will change, but when or if it will change soon.