"Do so" vs "do it"

Do so, do it, do that

We sometimes add so, it or that after the substitute do. Do so, do it and do that are sometimes used differently, but they are often interchangeable:

He said he was going to move to New Zealand and, to everyone’s surprise, he did so/did it/did that.

Do so

We use do so mostly to refer to actions where the subject and verb are the same as the ones we have mentioned. Do so is generally more formal than do it and do that:

I wanted them to leave, and politely asked them to do so, but they wouldn’t go, so I called the police. (I wanted them to leave and I politely asked them to leave.)

Warning:

Do so is more formal than do on its own:

A: Do you mind if I open the present now?
B: Yes, please do so. (Do so substitutes for open the present now)

We often use do so when we make a general reference to a series of actions or events:

The birds make their nests on the north side of the island in little holes in the rocks. The reason why they do so is because the south side of the island is exposed to extreme winds.

Do it

We use do it when we refer to an action or an event involving a verb and an object, especially when the subject is different from the one already mentioned:

A: He accidentally deleted some emails on his computer.
B: I do it all the time. (I delete files all the time.)

Do that

Do that is more emphatic and we use it for deliberate actions:

A: Would you ever give a complete stranger your phone number?
B: No. I would never do that. (I would never give a complete stranger my phone number.)

We often use do that in situations where we are contrasting things:

A: Would you like to have a few nights in a motel?
B: No, we’d prefer not to do that. We’d rather have a nice hotel. (We’d prefer not to have a few nights in a motel.)

A: I’ve decided to wait a year before starting college. I want to travel a bit and see the world.
B: I really think you should do that rather than starting college. You’re still so young. College will still be an option this time next year.

We can use a modal or an auxiliary verb + do to substitute for a main verb and what comes after it:

A: I feel terrible.
B: You should go to the doctor.
A: I should do, I know, but I have so much work to finish.

A: Has Martin met Paul before?
B: He could have done at the sales meeting last year, but I’m not sure.

Source: "Do" from English Grammar Today. Cambridge University Press.

Note that you could omit the "do so/it" phrase: "maybe I didn't have a reason to, either." In fact, you have emphasis-by-repetition if you say "I didn't have a reason not to...I didn't have a reason to..."

There is one time when we can say "I can so"

Brother: You can't go. Younger brother: I can so! Mother said I could!

NOTE: in USA, this "can so" construction is almost always used by children. Adults who use it are "acting childishly".

Both forms are acceptable, and 'do that' may be an alternative. The following extract may help:

Do so, do it, do that. :

The expressions do so, do it and do that are often used to avoid repeating a verb and its object or complement. These structures are rather formal.

• He asked me to get out and I did so without protesting.

• ‘Move those books off that chair.’ ‘I have already done so.’ (= I have already moved those books off that chair.)

• ‘Send them a fax.’ ‘I will do so.’ OR ‘I will do it.’

• I promised to buy her drinks and I did so. OR I promised to buy her drinks and I did it.

• I would like to ride a camel. I have never done that before. ‘I rode a camel during my trip to Morocco.’ ‘I would like to do that.’

Other verbs:

Only do can be followed by so, it and that in this way. We do not use these words after other auxiliary verbs. For example we cannot say, I can so or You must it. But we can say: I can do so or You must do it.

Source: http://www.englishgrammar.org/do-so-do-it-and-do-that/