Sure ! A lot of options there. CE's missions primarily are :
Mobility – clearing obstacles including minefields, destroying emplacements, bridging, making or improving roads, maybe clearing for an LZ, etc. I.e. improving mobility for friendly forces.
Counter-Mobility – emplacing obstacles, mines etc., bridge destruction, etc.,i.e. slowing of enemy forces, area denial, channelizing enemy movements, etc.
Vehicle recovery is not normally a CE mission, save for like all units. Recovering their own vehicles that are broken down, stuck, etc. That type of mission if it can't be done the unit's assets itself. Then higher level assets can be employed. Generally from the Bn's Maintenance Plt and it's own recovery assets. E.g. a Mech Bn when I was on active duty had :
2 Hvy Tracked Rec Vehs – M88s
6 Lgt Tracked Rec Vehs – M578s[these were usually attach to each Mech, Tank, etc., Company]
1 Wheeled Wrecker [forget the nomenclature … 
]
These are not CEs but Ordinance branch … [Ordinance guys don't favor being called CEs … and vis versa ! 
]
Just FYI …
But like I said, pretty much any unit will self recover their vehicles generally. If they can …
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