There can be a ton of them. Beer, Deer, Feel, etc.
Some four letter words with double Es are:aleebeefbeenbeepbeerbeetCreedeeddeemdeepdeerepeefeedfeelfeetfleefreegleeheedheeljeepjeerkeelkeenkeepkneeleekleermeekmeetneedpeekpeelpeerreedreefreekreelseedseekseemseenseepseerteentheetreeveerweedweekweepwhee
Four letter words with o e in the middle are: coeddoerdoesfoesgoergoeshoedhoerhoesJoeljoesjoeykoelnoelnoespoempoetroestoeatoedtoesvoeswoeszoea
tree
eggs
epee
Some four letter words with double Es are:aleebeefbeenbeepbeerbeetCreedeeddeemdeepdeerepeefeedfeelfeetfleefreegleeheedheeljeepjeerkeelkeenkeepkneeleekleermeekmeetneedpeekpeelpeerreedreefreekreelseedseekseemseenseepseerteentheetreeveerweedweekweepwhee
Some four letter words that start with E are:eachearneaseeasteasyechoecruedgeeditelseemitenvyepicetcheuroeveneverevilexamexit
bear
Some four letter words that have both A and E in them:acreaideareabakebalebarebasebeadbeambeanbeatcafecakecamecanecapecarecasedaledamedaredatedeaddealdeandeareachearlearneaseeasteasyelanfacefadefakefamefarefatefazefearfeatfleagalegamegapegategazegearharehatehavehazeheadhealheaphearheatideajadelaceladelakelamelanelatelazeleadleafleakleanleapmacemademakemalemanemarematemazemeadmealmeanmeatnamenapenearneatpacepagepalepaneparepatepavepeakpealpearpeatplearaceragerakeraperarerateraverazereadrealreamreaprearsafesagesakesalesamesanesatesavesealseamsearseattaketaletametapetareteaktealteamtearteatureavalevanevasevealwadewagewakewanewarewaveweakwealweanwearyearzeal
Four letter words with o e in the middle are: coeddoerdoesfoesgoergoeshoedhoerhoesJoeljoesjoeykoelnoelnoespoempoetroestoeatoedtoesvoeswoeszoea
envy
tree
Snidely Spellbinder wrote a four-letter word that begins and ends with e. With ease.
The word pies
eggs
There are no four letter words in English starting with e and ending in q.
epee