Lateraling from Regional Boutique

I'm currently an A1 at a regional boutique LMM bank, with the goal of eventually exiting to PE. I'm well aware that exit opps from a regional boutique to PE are very limited, so I would imagine lateraling to a more well known bank is a better bet. A few recruiters have reached out to me about lateraling, which is exciting. 

In your experience, how feasible is it to lateral to an EB or BB from a regional LMM boutique? Also, when would it be best to do so (i.e. as an A1 or A2 or..?) / start recruiting? 

thanks in advance!