How to vectorize a non-overlapped dataframe to overlapped shiftting dataframe?

I would like to transform a regular dataframe to a multi-index dataframe with overlap and shift.

For example, the input dataframe is like this sample code:

import pandas as pd
import numpy as np
df = pd.DataFrame(data=np.arange(0, 12).reshape(-1, 2), columns=['d1', 'd2'], dtype=float)
df.index.name = 'idx'
print(df)

Output:

       d1    d2
idx            
0     0.0   1.0
1     2.0   3.0
2     4.0   5.0
3     6.0   7.0
4     8.0   9.0
5    10.0  11.0

What I want to output is: Make it overlap by batch and shift one row per time (Add a column batchid to label every shift), like this (batchsize=4):

               d1    d2
idx batchid            
0   0         0.0   1.0
1   0         2.0   3.0
2   0         4.0   5.0
3   0         6.0   7.0
1   1         2.0   3.0
2   1         4.0   5.0
3   1         6.0   7.0
4   1         8.0   9.0
2   2         4.0   5.0
3   2         6.0   7.0
4   2         8.0   9.0
5   2        10.0  11.0

My work so far: I can make it work with iterations and concat them together. But it will take a lot of time.

batchsize = 4
ds, ids = [], []
idx = df.index.values
for bi in range(int(len(df) - batchsize + 1)):
    ids.append(idx[bi:bi+batchsize])
for k, idx in enumerate(ids):
    di = df.loc[pd.IndexSlice[idx], :].copy()
    di['batchid'] = k
    ds.append(di)
res = pd.concat(ds).fillna(0)
res.set_index('batchid', inplace=True, append=True)

Is there a way to vectorize and accelerate this process?

Thanks.