Can a pushdown automaton write more than one symbols on to stack on one reading from from input tape?

The formal definition of the pushdown automata according to Mike Sisper's book on theory of computation is as follows: . The transition function however only takes in one symbol from the stack (after popping it) and returns sets where each set only has a single letter from the stack alphabet.

But later in the book, it says this:

The PDA P begins by writing the start variable on its stack. It goes through a series of intermediate strings, making one substitution after another. Eventually it may arrive at a string that contains only terminal symbols, meaning that it has used the grammar to derive a string. Then P accepts if this string is identical to the string it has received as input.

It seems to say that the PDA is going to write more than one symbols in one reading of the input tape but how is this possible if the PDA can only write one symbol?

Based on the given definition, you cannot have a single transition that pushes multiple symbols from a single state. But you can simulate it. The idea here is to add auxiliary states and take advantage of $$\varepsilon$$ in the transition. Say you want to push $$abc$$ ($$c$$ will be the topmost symbol after) when reading $$1$$ from state $$q_i$$ going to $$q_j$$. Then modify your PDA so it will have the following transitions:
• $$\delta(q_i,1, \varepsilon) = \{(q_{i,0}, a)\}$$
• $$\delta(q_{i, 0}, \varepsilon , \varepsilon) = \{(q_{i,1}, b)\}$$
• $$\delta(q_{i, 1}, \varepsilon , \varepsilon) = \{(q_{j}, c) \}$$
The states $$q_{i,0}$$ and $$q_{i,1}$$ are auxiliary states. You can add more depending on how many stack symbols you want to push when reading a single input symbol.