Progressive Forms of May and Might
THE PAST PROGRESSIVE FORMS OF MAY AND MIGHT ARE FORMED BY ADDING HAVE BEEN + THE -ING FORM OF THE MAIN VERB.
--I didn't see them at the hotel. They may have been having dinner.
--The mail didn't arrive on time. The mailman might have been having trouble with his car.
THE PRESENT PROGRESSIVE FORMS OF MAY AND MIGHT ARE FORMED BY ADDING BE + THE -ING FORM OF THE MAIN VERB.

--We may be calling you in the morning.
--They might be visiting the U.S. this time next year.
NOTE: When must means necessity, the past form is had to. When it means probability, the past is must have + past participle.

Using Would
The modal auxiliary would is used in three different contexts:

1. EXPRESSING PREFERENCE:
--I would rather visit Los Angeles. (I'd rather... )
(Would rather means prefer.)
2. EXPRESSING REPEATED ACTION IN THE PAST:
--When she was alive, Aunt Stephanie would visit the West Coast.
(Would is used with regularly repeated actions in the past.)
3. POLITE REQUESTS
--I would appreciate hearing from you soon.
(Would is frequently used with polite requests.)

When used to express a repeated action in the past, would often takes the place of used to:
--When they were students, they would go skiing every winter.
ALSO:
--When they were students, they used to go skiing every winter.
However, when used to refers to a situation that existed (but was not necessarily repeated) in the past, would may not serve as a replacement:
--Aunt Stephanie used to live in Chicago.
NOT:
--Aunt Stephanie would live in Chicago.
Would can also be used in conditional sentences:
--If I had more time, I would read the instructions carefully.

Using Gerunds

A gerund is the -ing form of the verb used as a noun. Like nouns, gerunds can be subjects or objects:
SUBJECT GERUND:
--Playing golf is fun.
OBJECT GERUND:
--We're used to having a lot of fun.
In the second example, the gerund having is the object of the preposition to. This pattern is fairly frequent in English.
By is often used with gerunds to describe how something is done:
--By calling the office, you'll be able to know what's going on.
Here are a number of common verbs followed by gerunds:
finish--They finished working at 6 p.m.
stop--I stopped calling you at midnight.
quit--They quit eating for 24 hours.
avoid--You can't avoid answering the question.
keep (on)--They will keep on studying.
enjoy--My neighbor enjoys walking his dog.
appreciate--She would appreciate hearing from you.
mind--Do they mind selling their car?
NOTE: Go is followed by a gerund in certain idiomatic expressions related to sports and physical activities.
--Did they go shopping yesterday?
--They went sailing at the lake.
--We are going skiing this winter in the Rockies