I'd think about putting something to the side of the existing steps. My 5 year old contortionist can get in if it's the screen, but not main door for the same reason.
Maybe something like this if 18" will get him within reach of the door handle:
http://www.amazon.com/Range-Kleen-SS.../dp/B007EEG7M0
Or do a search on "pet stairs" for stuff that's taller.
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-Scott, DW, DG, DB, and DD
2011 Passport 2590BH
2009 Ford F150 SuperCrew F
X4 5.4L w/Max Tow