Constructing public key encryption schemes with desired ciphertext expansion I would like to know if 

given a public-key encryption scheme (PKES) with ciphertext expansion close to 1, and an integer N greater than or equal to 2

there exists a method for constructing a PKES with ciphertext expansion: 

size(ciphertext) = size(plaintext) x N


Preferably, the constructed PKES would be similar to the given PKES in terms of security and efficiency.

Thank you.

Edit [about padding][@poncho]: I work with two different entities represented as bitstrings. Let's call them large and small. 

size(large) = size(small) x N


Let encryption and decryption functions of the PKES be (E,D).

I receive many large bitstrings, and there is a need to store the small bitstrings which are derived as follows:

smallInstance = D(largeInstance)


At a later point, largeInstance should be recoverable using the public key:

E(smallInstance) = largeInstance


The problem I see with padding here is that it is not possible to use a constant padding for all the associated small bitstrings, and it is not desirable to store all the different paddings $pad_i$ obtained from:

smallInstance_i || pad_i = D(largeInstance_i)
From your expanded comments, it appears that you hope to use encryption to do data compression; that is, you have an $N$ Megabyte input, and hope to store it in a 1 Megabyte storage, and later recover it in toto.

Sorry, but that's (probably) impossible.  If there are $2^n$ possible largeInstance's, then you cannot store them in less than $n$ bits, and be able to recover it later.

The only case where it might be achievable is if the largeInstance's have a great deal of redundancy (and so that even though they are $n \times N$ bits long, only $2^n$ values are actually possible); if so, you'd be better off looking at a data compression method, rather than an encryption method.