In Act III Scene i Sir Anothony says:

But I have done with him; he’s anybody’s son for me. I never will see him more, never—never—never.

which seems to me to echo

King Lear's speech in Act V scene iii

And my poor fool is hang'd! No, no, no life!
Why should a dog, a horse, a rat, have life,
And thou no breath at all? Thou'lt come no more,
Never, never, never, never, never!

There is another King Lear allusion in Act III scene iv of The Rivals, when Bob ACres declares:

Zounds as the man in the play says, "I could do such deeds"

I think Bob is misquoting the bard here for in Act II scene iv of King Lear, Lear says

I will do such things

But it's typical of Bob's character to get it slightly wrong, don't you think?

In the same speech Bob also curses:

The thunder of your words has soured teh milk of human kindness

which is a direct allusion to Act I scene v of Macbeth. Lady Macbeth's speech includes this phrase:

Glamis thou art, and Cawdor; and shalt be
What thou art promised: yet do I fear thy nature;
It is too full o' the milk of human kindness
To catch the nearest way: thou wouldst be great;
Art not without ambition