Does adding more characters to the Enigma rotors improve crypto strength? This seems like an obvious question but I haven't been able to find it, so here goes:

Enigma is based on an alphabet of A-Z (26 characters); obviously this directly affects message content (e.g. numbers would be specified using their names one, four, two, etc) and it also has a direct bearing on the number of possible permutations (crypto strength).

Would increasing the alphabet of the rotors (e.g. to A-Z, 0-9, and a selection of special characters) increase crypto strength? I know it would increase the number of possible permutations but I'm not sure if that would introduce some kind of weakness.

Update (additional context)

I'm building a "for fun" software implementation of Enigma, in C# - currently as a UWP application that will run on any Windows 10 device (including phones).  It will include implementations of a few of the real-world historical Enigmas (I, M3, M4) as well as the ability to take "extended" Enigmas where you can create your own rotor sets with any number of rotors, including new wiring's and character sets (i.e. beyond A-Z).

Based on feedback provided adding additional characters could be dangerous.
I was thinking that for an 'extended' implementation you might want to include 0-9 and some special characters commonly used these days (such as : /).  I guess one motivation for this was convenience.  Of course given the flexibility of modern computing I guess I'd be better off allowing the user to input "convenience-plain-text" such as "HTTP : //WWW" transform it to "standard enigma A-Z plain-text" "HTTPCOLONBACKSLASHBACKSLASHWWW" then encipher it, and possibly perform the reverse at the other end.  Maybe that's the basis of further questions another time.

Update - 28-July-2017

Based on this Q&amp;A I can now actually measure the increase in key-size for enigma like systems; whilst expanding the supported character set does increase the key size, adding additional rotors increases it by significantly more (notwithstanding the other issues that affect the overall crypto-strength of enigma).
Does adding more characters to the (Enigma) rotors improve crypto strength?


Not really… since the weaknesses of Enigma go well beyond the count of chars per wheel! 

Of course you could – theoretically – think of using very big (read: huge) wheels with an insane char range. But, when looking at the “time” and “resources” you would need to invest each time you’ld merely wanted to encrypt and decrypt things with such a beast, it simply wouldn’t make much sense. Modern ciphers already blow Enigma out of the water in terms of speed, cryptographic-strength, etc.

Differently stated: the gain you would achieve by adding chars won’t be big enough to level-up good old Enigma into the realms of more recent and better preforming algos (like aes, chacha, et al). 

Also, as CodesInChaos already hinted in his comment, it would put you on a very slippery road with a good chance that you’ll end up introducing additional attack vectors. In a worst case, you could break one of the stronger parts of Enigma while ignoring the real cryptographic weaknesses that already come with Enigma; which would result in something like a (let’s just call it) cryptographic nightmare.

Yet, don’t get me wrong: for something like a non-public “student project” with the goal to have a truckload of chances to shape your cryptanalytic abilities… this could be fun to fiddle with and maybe worth thinking about for a minute. But if you do, you better be prepared to notice you’ll need to fix a whole truckload of nasty little issues related to Enigma. Simply increasing the char count will not do it.