The following will produce the same result (a conditional infinite loop):

{@x&&redo}
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If you're asking if it's possible to use more than one statement modifier in a statement, it's not in Perl5. Quote perlsyn (emphasis in original):

Any simple statement may optionally be followed by a SINGLE modifier, just before the terminating semicolon (or block ending).

If you want to use lots of whiles in a code, define a sub. For example (untested):

sub w (\&@) { while (&{$_[0]}()) { &{$_[1]}() } } 
sub d (\&) { $_[0]; }
# then, instead of while (foo) { bar }, you can say
w{foo}d{bar};
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sub l(\&) { WHILE: while(1) { &{$_[0]}(); } }
sub w($) { $_[0] or last WHILE }
# then, instead of while (foo) { bar },
l{w foo;bar};
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Bugs:

• The proto is &, not \&.

Golf

• The label is not needed in the second snippet.
• x->() is shorter than &{x}().
• &{x} is even shorter if you don't care about @_.
• y while x is shorter than while (x) { y }.
• {x;redo} is shorter than x while 1.
• || is shorter than  or.
• Proto not needed for w in second snippet.

sub w(&$){&{$_[1]}while&{$_[0]}}sub d(&){$_[0]}
# then, instead of while (foo) { bar },
w{foo}d{bar};
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sub l(&){{&{$_[0]};redo}}sub w{$_[0]||last}
# then, instead of while (foo) { bar },
l{w foo;bar};
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• The proto is &, not \&.

True. I keep messing this one up.

• x->() is shorter than &{x}().
• y while x is shorter than while (x) { y }.
• || is shorter than or .
• The label is not needed in the second snippet.

Yep. I thought of the case when you need lots of while loops, so the size of the definition doesn't really matter, only the way you use them.

• {x;redo} is shorter than x while 1.

Doesn't help here anymore I guess, because we have nonalnums around while.

• &{x} is even shorter if you don't care about @_.

Yes, but that doesn't really help because you don't get the @_ of the loop context, only the @_ passed to w or l.

While we're there, &{+pop} is even shorter than &{$_[0]} in the defn of l, and pop is shorter than $_[0] in w.

• Proto not needed for w in second snippet.

It puts the condition in scalar context, like while does, so it might save some characters in the loops.