Can banks 'create' money on their own or do they need help from other banks? My current understanding of the banking money multiplication process goes as follows: Alice comes along and deposits 100 cash into Bank A. Bank A gains 100 in vault cash (reserves) as an asset and 100 in liabilities in the form of Alice's checkable deposit. Bank A then loans out 90 (they cannot loan more since RR=0.1) and so the banks asset are 10 reserves and 90 loans and everything balances. The individual who gets the loan from Bank A takes the 90 and deposits in say Bank B and the multiplying process continues until total nation-wide deposits=10*reserves=$1000.
But now my textbook (Mishkin) states that

Because a single bank can create deposits equal only to the amount of its excess reserves, it cannot by itself generate multiple deposit expansion.

He then goes on to say that

A single bank cannot make loans greater in amount than its excess reserves

as well as

the banking system as a whole can generate a multiple expansion of deposits, because when a bank loses its excess reserves, these reserves do not leave the banking system, even though they are lost to the individual bank

But this doesn't make sense to me at all. I see no reason why Bank A in my earlier example is not able to multiply deposits all on its own. Say that in my example, the original 90 loan goes out to Bob to finance one of his business endevours. Bob does not want 90 in cash so instead he opens up a checkable deposit account at bank A and so bank A's reserves go back to 100 with 90 in loans and now they have deposits =190 . Clearly they have excess reserves. So they now make another loan to Mary equal to to 81 who then also does not wish to hold cash and so she stores the money in a deposit account at bank A. This process then repeats as Bank A makes loans and each borrower gets a deposit at bank A until bank A has 100 in reserves, 900 in loans and 1000 in deposits.
Thus Bank A, a single bank, has generated multiple deposit expansion. But Minkish seems to say this is only possible if the borowers deposit their money in other banks instead of the original lending bank. So is he wrong or am I wrong and missing something here? Any help on this would be most appreciated!
The question in the title is actually a bit broader than the question in the body, I will try to answer both questions starting with the one in the title.
Answer to Question in the Title

Can banks 'create' money on their own or do they need help from other banks?

Yes, banks actually can crate deposits on their own without help of other banks, thanks to getting excess reserves in the interbank market or from central bank. For example, you can have look at McLeay (2014) Money creation in the modern economy which explains that in greater detail, and it will likely be covered in later chapters in the textbook unless it is old one (or you can have look at other textbooks such as Blanchard et al Macroeconomics a European Perspective).
Answer to the Question in the Body
In the body your question is about whether single bank can increase money supply within the money multiplier model. There the answer is no.
The multiplier model is one model of money creation that applies under certain circumstances, such as when central banks decide to exogenously control money supply by changing quantity of reserves (although the money multiplier exists in multiple models usually when people talk about money multiplier they talk about the simplest exogenous supply of money model). But the multiplier model won't hold (save for special cases) when the central bank conducts its policy through setting interest rate and supplying amount of reserves that is demanded.
This is because if there is only single bank it won't be able to create more reserves out of new deposits For example, let us assume that single bank starts with 100 reserves (R), which are assets  and 100 deposits (D) which are liabilities. The ballance sheet of such bank will look like:
  Bank A
   A | L
 -----------
100R | 100D

Now if bank issues a loan that means that it is converting some of the reserves to a loan. If a single bank would issue a loan and the person would kept the loan with the same bank then the balance sheet would look like this:
  Bank A
   A | L
 -----------
 10R | 100D
 90L |

And bank would not be able to lent any more money as with 10% reserve ratio it would already issue the maximum amount of loans it can make as it has no more excess reserves to lent out. However, the 90 loan that exists the bank can then become a reserve for a new bank, so for bank B the balance sheet would look like:
   Bank B
   A | L
 -----------
 90R | 90D

Hence now that original 90 loan became new 90 reserve and that would not happen if the original bank would just keep the money. Now the new bank can further break the 90R into 10R and 80L and so on.
Now as mentioned in the first paragraph the above won't hold in practice as even single bank nowadays can support more lending by getting excess reserves from other banks  or when central bank is willing to supply additional reserves instead of just setting the quantity reserves from the get go. Nowadays central banks mainly change the price for reserves (i.e. the interest) not amount of reserves. In that case that single bank can just increase the amount of R to create new loans (and matching deposits). However, even that is currently no longer the case because reserve requirements were dropped by Fed in 2020 so now banks can lend as much as they can (at least in US and other countries).
The multiplier model is a simplification that is mostly used as an introduction to money creation since it is an exogenous money supply model and those are easier to solve and learning the more nuanced endogenous money supply model is easier after learning the exogenous one. I am not sure to which Mishkin textbook you refer to, but I would be surprised if in later chapters it would not cover endogenous money supply models (money multiplier is an exogenous money supply model). For example, textbook by Blanchard et al. covers endogenous money supply model right after money multiplier, unless the Mishkin textbook you refer to is very old (prior 2009) it will likely cover it as well in subsequent section.