Can a player swap more than 4 resources of the same kind with another player
There is nothing in the rules that prohibits this move.

The following excerpts are taken from the 5th edition rules.

Page 7, "Domestic Trade":


  On your turn, you may trade resources with the other players (after rolling for resource production).  You and the other players negotiate the terms of your trades - such as which cards will be exchanged.  You may trade as many times as you can, using single or multiple cards.  However, you cannot give away cards, or trade matching resources ("trade" 3 or for 1 ore, for example).


Page 14, "Trade":


  After you roll for resource production, you may trade with other players (domestic trade) or with the bank (maritime trade).
  
  
  You may trade as long as you have resource cards.
  If you decide not to trade during your turn, no one can trade.
  You may trade with another player between your turns, but only if it is his turn and he elects to trade with you.
  You may not trade with the bank during another player's turn.
  You may not give away cards.
  You may not trade development cards.
  You may not trade like resources (e.g., 2 wool for 1 wool).
  


There is no mention of restrictions on the number of cards that can be traded in a single move.