Sure. There are lots of ways to handle it. First, I presume that "he" and "she" have names, right? Here are a couple of ways to handle the issue:
Here's the issue:
"He went to the store to buy bread and, while there, also purchased ice."
Here are three possible solutions:
"Bob went to the store to buy bread and, while there, also purchased ice."
"The ice was probably going to be a bag of water by the time he got home from the store with the bread."
"
Just great! Now I have ice, but still no bread. What a wasted trip to the store."
See how easy? The first one relies on using the name, instead of he said, she said. The second proposes the
action of the ice melting, and the bread is an afterthought. The third one drops into "deep point of view" by directly relaying Bob's thoughts to the reader (perfectly acceptable in third person). It also makes the original trip to buy bread a springboard for the next scene of going to a second store.
All of the methods relay the same information of the original sentence, but have the ability to advance the plot or advance the character (being annoyed) as well.
Hope that helps!