I have 5 cats....They all had problems when they were first introduced to
the others. I simply yelled at both of them, and clapped my hands together
and scared them out of the room elsewhere whenever they showed signs of
fighting. - Pretty soon, they realized that I didn't like it, and it wasn't
worth it, so they learned to get along. Now, they seldom hiss at one
another, and sometimes they even play together. Your kittens will grow up
fast.....In a few weeks they will be large enough to take care of
themselves. In the meantime, let them all know that you won't put up with
them fighting with one another.......

I have 3 - the latest was a kitten when he came here 10 yrs ago and the other
two were 6 yrs at the time.  They hated the new kitten and would hiss and
avoid him or give him a smack or two.  Now they have all learned to tolerate
each other but it took quite awhile.  They may never be "friends" and sleep
cuddled up together; being able to tolerate each other is about the most you
may get but there's nothing wrong with that.  You need much more time than 2
weeks; eventually Lilli will calm down and realize the kittens are there to
stay.  If it's any consolation, my guys have been living together for almost
10 yrs and they still hiss once in awhile.  I wouldn't start yelling at them -
can cause stress for the adults and they are already under enough stress with
the new additions; just clap your hands if they start to fight or you could
try "growling"; it actually works - mama cat growls at her kittens when she's
mad at them so they associate you growling with that.  

Riannon

PS  Don't forget you will need 3 or 4 litter boxes for 4 cats

Why do people do this?  Cats are like people.    Some personality types
simply don't like other personality types.  If you're going to get more than
one cat, you might be better off getting one of the same breed (or you might
call it race) as the first one for a better chance of acceptance.

It's a good idea to try the new cat out for a couple of weeks first as well,
to see if they will get along.  Remember, the first cat thinks the house
belongs to him/her.  Other cats are intruders.

Note also that two female cats tend to get along with each other overall
better than a male and female (because even fixed males will bother females
to no end sexually)
and better than two males (because males are both possessive and want
domination).

Also, older cats feel threatened by kittens, (including their own) after a
few weeks.   They are fearful that you will show preference to the kittens
(which usually is the case) and shortly get rid of them.    It's also
irritating to their nerves to have the young little pranksters jumping
around all the time.    You probably won't like that either when you are
old.  Older cats also tend to prefer homes that are more quiet and where
they can do their own thing in peace.  They want basically what exactly what
most older people want.

As a person who once owned 6 cats, I can tell you that that's far too many.
No home should have more than two at very most.  Owners should also be
prepared to keep and love those cats for 20 years or so, because it's really
hard for an older cat to adjust when it's simply shoved into a new home
again.  This can be terrifying and very upsetting for them.
____________________________________________

You've gotten lots of suggestions which are all potentially valid.  I
just wanted to add one thing.  Sometimes, cats need to work out their
own politics, and our interference is not always welcome.  As long as
you are there in the background to defuse any potentially dangerous
situation for the little ones, you might want to sit back and watch
them work out their own pecking order.  They have rules and
communications we do not always understand and if we stay out of the
way, they can sometimes settle themselves much more quickly.  I have
seen this work several times.  Other times, we need to mediate, but if
nothing else works, you might want to step back and see if they can
work it out.  As I said, always staying close enough for a quick
rescue of a kitten just in case it gets nasty.

I have used this method for 24 years and it has not failed yet.  The
other thing I do is give each and every cat total coddling whenever I
get one in a room by himself, without the others to see or get
jealous, so that they are each still secure in my affections.  It has
even worked with my current pair, one of which was 13 years old when
the other was acquired as a new kitten and severe jealousy ensued.  At
first, it was the kitten in jeopardy, and then when he grew into a 16
pound man'o'war, it became the fragile old lady cat who was
vulnerable.  But now they have a nice parallel existence and even
vacate my lap for the other when the rival comes in the room.  All
civil and courteous now but what a war zone it was in the first
months!

Good luck

--tension