Given two modules $M$ and $N$ there is a nice scheme parametrizing extensions

$0 \rightarrow M \rightarrow E \rightarrow N \rightarrow 0$

namely $Ext^1(N,M)$ or, leaving out the trivial extension, the projective space $P(Ext^1(N,M))$.

There are (at least) two natrual generalizations

1. n-step extensions

   $M \rightarrow E_1 \rightarrow E_2 \rightarrow \dots \rightarrow E_n \rightarrow N$

   between $N$ and $M$.

2. Filtered modules: Parametrize modules $E$ which admit a filtration

   $0 \subset F_1 \subset F_2 \dots F_n=E$

   with fixed graded objects $E_i=F_i/F_{i-1}$.

I suppose in the first case one can use the group Ext^n(M,N), although I never saw a construction of a universal family. Is there a good reference?

In the second case, I do not have a clue. So my main question is:

Is there a nice moduli space of filtered objects?

Given two modules $M$ and $N$ there is a nice scheme parametrizing extensions

$0 \rightarrow M \rightarrow E \rightarrow N \rightarrow 0$

namely $\operatorname{Ext}^1(N,M)$ or, leaving out the trivial extension, the projective space $P(\operatorname{Ext}^1(N,M))$.

There are (at least) two natural generalizations

1. $n$-step extensions

   $M \rightarrow E_1 \rightarrow E_2 \rightarrow \dots \rightarrow E_n \rightarrow N$

   between $N$ and $M$.

2. Filtered modules: Parametrize modules $E$ which admit a filtration

   $0 \subset F_1 \subset F_2 \dots F_n=E$

   with fixed graded objects $E_i=F_i/F_{i-1}$.

I suppose in the first case one can use the group $\operatorname{Ext}^n(M,N)$, although I never saw a construction of a universal family. Is there a good reference?

In the second case, I do not have a clue. So my main question is:

Is there a nice moduli space of filtered objects?