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Many of us have 20+ cards active.
It’s pretty much inevitable when you go full throttle into this game.
So yes you can but once again you need to be strategic about this.
Each bank can and does have its own rules.
For example, Chase has 5/24 and Amex has its 1 bonus rule per card and now rolling out card family bonus restrictions for Delta and personal Blue family cards.
Citi has 24 & 48 month sign up bonus restrictions and so on.
As far as opening and closing cards that too has to be done strategically as you want to make sure to keep 1-3 of your oldest cards so that your credit history length remains high and pull up your average card history age as you add more and more new cards.
You generally want to downgrade a card, hopefully to a free one, instead of close unless there is a reason to actively close it.
Always keep a card open for a full year before doing any downgrades or closures.
Frequent closures will be noted by the bank labeling you as a card churner which generally isn’t profitable for a bank.
After 2-3 years you’re ok to close a card.
As for the biz card with the associated business no longer existing you should technically close it but if it is tied to your personal credit there really isn’t much use in closing it.
Just use it as you’re still the one paying the bill and ultimately responsible for the card.
But it does give you a reason to open new biz cards as you start your new biz and “close” your older ones (excuse given to bank if they inquire why you need more cards).